In this paper, we propose a novel stochastic model to study prime distribution in almost-short intervals, inspired by a corollary of the Maynard-Guth theorem. The model uses the equation \[ x_{n+1} = x_n + \frac{y}{\log x_n} + \epsilon_n, \] where \(\epsilon_n\) follows a Laplace distribution, and demonstrates that our new bound surpasses both Walfisz and Maynard-Guth bounds, particularly for large \(x\): \[ \left| \pi(x + y) - \pi(x) - \frac{y}{\log x} \right| \leq C \cdot y \exp(-\sqrt[4]{\log x}). \] Additionally, we explore a modulated Hamiltonian \(\hat{H}(x)\), derived from a potential \(V(x)\) and a test function \(f(x)\), that exhibits behavior akin to the energy levels of the heavy nucleus \(H_{38}\). The gaps between these energy levels resemble the distribution of zeros of the Riemann zeta function near the critical line, suggesting that \(\zeta(0.5 + i \hat{H}(x))\) corresponds to the energy levels of \(\hat{H}(x)\), thus supporting a quantum mechanical interpretation of the Riemann hypothesis. Furthermore, assuming the Elliott-Halberstam conjecture, which implies that prime gaps can be as small as 12, we find that the transition rate \(\Gamma_{p \to p+12}\) between quantum states associated with prime numbers increases with larger primes. This observation indicates that the distribution of prime gaps reflects an underlying discrete structure in the "energy" landscape of primes, offering a novel perspective on the connection between number theory and quantum physics.

With the advent of Web 3.0, the swift advancement of technology confronts an imminent threat from quantum computing. Security protocols safeguarding the integrity of Web 2.0 and Web 3.0 are growing more susceptible to both quantum attacks and sophisticated classical threats. The article introduces our novel long-distance free-space quantum secure direct communication (LF QSDC) as a method to safeguard against security breaches in both quantum and classical contexts. Differing from techniques like quantum key distribution (QKD), LF QSDC surpasses constraints by facilitating encrypted data transmission sans key exchanges, thus diminishing the inherent weaknesses of key-based systems. The distinctiveness of this attribute, coupled with its quantum mechanics base, protects against quantum computer assaults and advanced non-quantum dangers, harmonizing seamlessly with the untrustworthy tenets of the Web 3.0 age. The focus of our study is the technical design and incorporation of LF QSDC into web 3.0 network infrastructures, highlighting its efficacy for extended-range communication. LF QSDC is based on the memory DL04 protocol and enhanced with our novel Quantum-Aware Low-Density Parity Check (LDPC), Pointing, Acquisition, and Tracking (PAT) technologies, and Atmospheric Quantum Correction Algorithm (AQCA). Utilizing this method not only bolsters the security of worldwide Web 3.0 networks but also guarantees their endurance in a time when quantum and sophisticated classical threats exist simultaneously. Consequently, LF QSDC stands out as a robust security solution, well-suited for Web 3.0 systems amidst the constantly evolving digital environment.

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

Drug discovery and development is a highly complex and costly endeavor, typically requiring over a decade and substantial financial investment to bring a new drug to market. Traditional computer-aided drug design (CADD) has made significant progress in accelerating this process, but the development of quantum computing offers potential due to its unique capabilities. This paper discusses the integration of quantum computing into drug discovery and development, focusing on how quantum technologies might accelerate and enhance various stages of the drug development cycle. Specifically, we explore the application of quantum computing in addressing challenges related to drug discovery, such as molecular simulation and the prediction of drug-target interactions, as well as the optimization of clinical trial outcomes. By leveraging the inherent capabilities of quantum computing, we might be able to reduce the time and cost associated with bringing new drugs to market, ultimately benefiting public health.

A simple model of a measurement in a laboratory isolated from the environment is analyzed in detail, demonstrating the features of the collapse effect. Such an experiment can readily be implemented today under the idealization of an observer's memory as a simple quantum system. The central role of loss of information is emphasized.

Two approaches are being proposed to complements existing practical implementations of quantum information processing; (a) Multiplexed Michelson interferometry for Linear Optical quantum computation which should in principle split further an initially split beam to yield new sets of beams which are scalable to multiple interferometric outputs beyond just the dual output in Mach Zehnder interferometry. Generally Interferometry is applied in quantum computation particularly linear optical quantum computation schemes such as K.L.M protocol using the Mach-Zehnder interferometer, however a multiplexed Michelson interferometry enables the production of scalable cross-correlated beams making it suitable for optical multi-qubit operations. (b) Coupled LDR Circuits for Quantum emulation which can model cross correlation and probabilistic qubit states to enable parallelization and Gating on Classical electrical circuits. The system is to be designed as a network of electrical circuits coupled to each other using electrical coupling elements and are equipped with a light dependent resistor (LDR) alternatively referred to as photo-resistor to provide variable resistance in response to varied intensity of incident light. The maximum threshold current state which is being defined for the circuit and a minimum current state corresponds to 1 and 0 binary states respectively, however an intermediate current state models a superposition of 1 & 0. Likewise varying the intermediate current values closer to either 1 or 0 is akin to a probability rotation of the qubit states which is achieved by varying resistance using the LDR where the multi-circuit coupling interaction helps emulates cross-correlation of multi-qubit systems. The proposed system can be useful at least as a tool for informative applications in a classical framework.

This paper contains a comparative review of existing Zitterbewegung models. It attempts to synthesize them by offering a toy model containing an extra hypothesis of electromagnetic self-oscillation at the Fermi scale (10−15m). Inspired by Bell violation experiments, Zitterbewegung models and hydrodynamic walker studies, we revisit standing waves in quantum mechanics, echoing de Broglie-Bohm pilot wave theories. Starting with the electromagnetic self-oscillation hypothesis at the Fermi scale we propose an emergent and deductive hierarchical electron structure across multiple scales. The model spans Fermi, Compton (10−13m), Bohr (10−11m) and finally de Broglie (>10−10m). At the Fermi scale, the hypothesis is one of "source-free chiral light", known as the "zilch", emerging as a self-oscillating electromagnetic field at the Schwinger limit. This self-interaction of retarded potentials due to real relativistic delays is a generic self-oscillation of Liénard-Wiechert potentials. This primary Fermi oscillation accounts for charge and mass at the Fermi scale. It generates secondary stable "auto-orbits" dynamics at the Compton scale, manifesting as observable spin and other quantum properties of the usual Dirac zitterbewegung models. These zitter models account for known electron characteristics, including mass, charge, spin and g/2 anomalous factors up to 9 digits precision. We explain the de Broglie wavelength through Doppler-shifted Compton-scale standing waves, in the tradition of de Broglie. The framework extends to electron-positron pair production at the Schwinger limit, described as a result of natural light focusing in non-homogeneous media, utilizing René Thom’s catastrophe theory. This offers a new perspective on baryogenesis and matter emergence from electromagnetic fields. We dub this toy model the "sub-standard" model of the electron.

In this paper, we investigate various graphene monolayer nanomesh structures (diodes) formed only by nanoholes, with a diameter of just 20 nm and etched from the graphene layer in different shapes (such as rhombus, bow-tie, rectangle, trapezoid, and triangle), and their electrical properties targeting electromagnetic energy harvesting applications. In this respect, the main parameters characterizing any nonlinear device for energy harvesting are extracted from tens of measurements performed on a single chip containing the fabricated diodes. The best nano-perforated graphene structure is the triangle nanomesh one, which exhibits remarkable performance in terms of its characteristic parameters, i.e., a 420 Ω differential resistance for optimal impedance matching to an antenna, a high responsivity greater than 1000 V/W, and a low noise equivalent power of 847 pW/√Hz at 0 V.

Changing the symmetry of spin from SU(2) to the quaternion group, $Q_8$, has a number of ramifications. In this paper we first summarize the properties of Q-spin and then discuss some of those resulting changes. Many are counter to well-established ideas which change our view of the microscopic.

Quantum observers, agents whose entanglement with a measured system may remain coherent, are analyzed in a consistent approach. Thought experiments, including one by Deutsch and one by Frauchiger and Renner, are discussed and modeled using quantum circuits. Terminology is suggested which helps avoid contradictions.

Reduction of the density operator for quantum subsystems is derived without the use of the Born Rule.

Barium monofluoride (BaF) is a polar molecule of interest to measurements of the electron electric dipole moment [1, 2]. For this purpose efforts are under way to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne [3]. For a theoretical understanding of the electronic structure of such an embedded molecule the need arises for efficient methods which are accurate, but also can handle a number of atoms which surround the molecule. The calculation for gas-phase BaF can be reduced to involve only outer electrons by representing the inner core of Ba with a pseudopotential [4] while carrying out a non-relativistic calculation with an appropriate basis set [5]. In this work we demonstrate to which extent this can be achieved using coupled-cluster methods to deal with electron correlation. As a test case the SrF(X 2Σ+ → B 2Σ+) transition is investigated and excellent accuracy is obtained with the EOM-CC3 method. For the BaF(X 2Σ+ → A′ 2∆, X 2Σ+ → A 2Π, X 2Σ+ → B 2Σ+) transitions various coupled-cluster approaches are compared with very good agreement for EOM-CC3 with experimentally derived spectroscopic parameters except for the excitation to the A′ 2∆ state for which the excitation energy is overestimated by 200 cm−1.

Magnesium monofluoride is a polar molecule amenable to laser cooling which has caused renewed interest in its spectroscopy. In this work we consider the case of three low-lying electronic excitations, namely $\rm X \, {}^{2}\Sigma \to A \, {}^{2}\Pi, \ \to B \, {}^{2}\Sigma, \ \to C \,{}^{2}\Sigma$, using well developed quantum chemistry approaches, i.e., without reference to the spin-orbit splitting of the $\rm A \, {}^{2}\Pi$ states. Accurate experimental data for these transitions have been available for over 50 years. Here we explore the linear response method at the level of CC2 theory, as well as equation of motion methods at the level of CCSD and CC3, using two families of basis sets. Excellent agreement is obtained for the first three transitions when using the correlation-consistent basis sets and extrapolation to the complete basis limit within EOM-CC3 (at a relative precision of $10^{-4}$), and qualitative agreement for the other two methods. The purpose of this paper is to serve as a guide in how to approach the accurate calculation of excitations in polar diatomic molecules.

The locality condition of probabilities underpinning the derivation of Bell inequalities can be violated classically. The wave function collapse of an entangled state of single photons results in the factorization of quantum probabilities. It is possible to differentiate, locally, between ensemble probabilities of single detections with and without wave function collapse for the alleged quantum nonlocality. The theoretical concept of photonic quantum nonlocality cannot be implemented physically because of the quantum Rayleigh scattering of single photons. A distinction needs to be made between the correlation of individual, single measurements of pure states and the correlation of the measurement ensemble of the mixed states. The correlation operator of Pauli vector operators delivers the same probabilities of correlated detections of photons for both independent and multi-photon states as for ‘entangled’ states of photons. As single-photon sources are not needed, the design and implementation of quantum computing operations and other devices will be significantly streamlined.

Digitized counter-diabatic (CD) optimization algorithms have been proposed and extensively studied to enhance performance in quantum computing by accelerating adiabatic processes while minimizing energy transitions. While adding approximate counter-diabatic terms can initially introduce adiabatic errors that decrease over time, Trotter errors from decomposition approximation persist. On the other hand, increasing the high-order nested commutators for CD terms may improve adiabatic errors but could also introduce additional Trotter errors. In this article, we examine the two-qubit model to explore the interplay between approximate CD, adiabatic errors, Trotter errors, coefficients and commutators. Through these analysis, we aim to gain insights into optimizing these factors for better fidelity, shallower circuit depth, and reduced gate number in near-term gate-based quantum computing.

In previous papers we have shown how Schr\"{o}dinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is drived by information and not only electromagnetic fields. This program was applied also to Pauli's equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and energy, describe observational data more effectively, and formulate quantum gravity. In addition, despite the immense success of the quantum field theory, the framework requires renormalization techniques and breaks down at high energies. Recently, the Planck legacy 2018 release has confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level higher than 99%. This study considers the implied curvature of the early Universe as the curvature of “the background or 4D conformal bulk as a manifestation of vacuum energy” and distinguishes it from the localized curvature that is induced in the bulk by the presence of celestial objects that are regarded as ”4D relativistic cloud-worlds.” Analogously, because gravity appears to emerge owing to spacetime curvature and does not exhibit critical characteristics shared by other fields, it has been incorporated as the local curvature of the bulk affecting the embedded quantum fields that are regarded as propagating “4D relativistic quantum clouds.” To consider the effects of the bulk on embedded clouds, this paper presents interaction field equations in terms of brane-world modified gravity and the perspective of geometrization of the quantum mechanics wherein gravity is manifested by the curvature of 4D conformal bulk as an indicator of the field strength of vacuum energy on the embedded 4D relativistic clouds in addition to the boundary interactions, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic cloud-worlds over the conformal spacetime of the 4D bulk is presented, whereas the standard said theories can be recovered from the interaction field equations.

We propose a novel approach to quantum theory construction that involves solving a maximization problem on the Shannon entropy of all possible measurements of a system, relative to its initial preparation. This maximization problem is additionally constrained by a phase condition that vanishes under measurements. Specifically, enforcing a vanishing U(1)-valued phase constraint leads to standard quantum mechanics, while a vanishing Spin^c(3,1)-valued phase constraint extends the theory to relativistic quantum mechanics and to quantum gravity. The latter scenario derives the metric tensor as an operator via a double-copy mechanism applied to the Dirac current. Significantly, this solution is consistent exclusively in 3+1-dimensions as all other dimensional configurations lead to fundamental obstructions. Finally, the solution uniquely incorporates the SU(3)xSU(2)xU(1) symmetries of the Standard Model. This framework seamlessly integrates fundamental concepts from quantum mechanics, relativistic quantum mechanics, quantum gravity, the dimensional specificity of spacetime, and particle physics gauge symmetries as the solution to a simple entropy optimization problem.

{We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of $\frac{1}{2}$—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of $\frac{1}{2}$, or it remains a boson and precesses without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, $Q_8$, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion is the reason for the observed violation of Bell's Inequalities and resolves the EPR paradox.

Quantum theory predicts violations of Bell’s inequality. This implies a contradiction with at least one of three statistical conditions, known as “Realism” (joint distribution of relevant observables), “Locality” (conditional separability of pairwise observations, given a set of hidden variables), and “Free Will” (statistical independence between hidden variables and measurement settings). Here we describe a classical system with “clockwork” properties that is unquestionably local. It produces maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It contradicts every one of the three listed formal conditions. Nonetheless, it expresses the qualitative markers of ontological Realism, ontological Locality, and ontological Free Will, all at the same time. In other words, the three listed conditions do not correspond to the three ontological concepts with the same names. Therefore, there is no conflict between quantum theory and Local Realism.

This paper discusses the Quantum Temporal Resonator (QTR), a theoretical device leveraging quantum entanglement and metamaterials with negative refraction indices to achieve controlled temporal displacement. By establishing a network of entangled particles within a Bose-Einstein Condensate (BEC) and utilizing a resonant cavity made of advanced metamaterials, the QTR creates localized distortions in space-time. The frequency and amplitude of temporal harmonics within this cavity are finely tuned to allow for precise temporal displacement of matter and information. Numerical simulations demonstrate the coupling between the quantum wave function and electromagnetic fields, validating the theoretical model. The results show distinctive patterns in the wave function and perturbations in the electric field, supporting the feasibility of achieving controlled temporal displacement. This study explores the theoretical framework, mathematical modeling, experimental setup, and potential applications of the QTR, providing a comprehensive analysis of its feasibility and implications.

The mechanism by which the human nose perceives an odor is complex and involves various chemical reactions in the transformation of the odorous molecule into an electrical impulse sent to the brain that returns the sensation of smell. The smell is classified and quantified, and its instrumental detection can be carried out through the “electronic nose”, an interactive device that lends itself to various applications. In the agri-food sector, the development of portable devices makes possible to smell foods and measure their level of deterioration and maturation; this is undoubtedly useful for reducing waste, identifying the best moment for food consumption, and improving the level of food safety. With regard to the environmental compatibility of materials and techniques for packing and laying conglomerates (for example bituminous), the problem of olfactory nuisance for the population residing in the neighborhood is still an unresolved problem. The approach based on electronic noses is very effective. The electronic nose also represents an important resource in the screening of respiratory pathologies, where there is the need to identify a rapid and reliable diagnostic test for pathologies such as pneumonia or seasonal flu. Environmental monitoring of pollutants is of particular relevance today and the electronic nose is an important candidate for the use in this field. The gas sensor market leverages physics, chemistry and materials engineering to develop highly sensitive, reliable and stable sensor platforms, capable of detecting very small amounts of gas molecules in the environment. To develop competitive gas sensing platforms, new materials are being considered, including polymers, nanostructured metal oxides and nanostructured carbon-based materials (CNTs). In addition to the experimental aspects, in particular Raman and electron spectroscopy techniques together with atomic force microscopy, theoretical-mathematical modeling plays an extremely important role in this sector, with particular attention to the case of micro and nanometric dimensions. Many efforts are now aimed in improving the sensitivity of these devices and this is related to the diffusion of carriers in them. The paper also offers an overview of the mathematical models relating to mechanical processes and dynamics at the micro-nanometric scale, lastly focusing on the Drude-Lorentz type models, with related more recent generalizations.

Investigations into the properties of generalized effective temperature are conducted across arbitrary dimensions. Maxwell-Boltzmann distribution is displayed for one, two, and three dimensions, with effective temperatures expressed for each dimension. The energy density of blackbody radiation is examined as a function of dimensionality. Effective temperatures for non-uniform temperature distributions in one, two, three, and higher dimensions are presented, with generalizations extended to arbitrary dimensions. Furthermore, the application of generalized effective temperature is explored not only for linearly non-uniform temperature distributions but also for scenarios involving the volume fraction of two distinct temperature distributions. Finally, the effective temperature is determined for a cryogenic system supplied with both liquid nitrogen and liquid helium.

TThe locality condition of probabilities underpinning the derivation of Bell inequalities can be violated classically. The wave function collapse of an entangled state of single photons results in the factorization of quantum probabilities. It is possible to differentiate, locally, between ensemble probabilities of single detections with and without wave function collapse for the alleged quantum nonlocality. The theoretical concept of photonic quantum nonlocality cannot be implemented physically because of the quantum Rayleigh scattering of single photons. A distinction needs to be made between the correlation of individual, single measurements of pure states and the correlation of the measurement ensemble of the mixed states. The correlation operator of Pauli vector operators delivers the same probabilities of correlated detections of photons for both independent and multi-photon states as for ‘entangled’ states of photons. As single-photon sources are not needed, the design and implementation of quantum computing operations and other devices will be significantly streamlined. © 2024 The Author

Under the quaternion group, $Q_8$, spin helicity emerges as an element of reality, and complementary to spin polarization. Here we show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet, being divided between polarization and coherence. Including helicity accounts for the violation of Bell's Inequalities without non-locality.

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasi probability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.

Particles are considered temporarily identical if the interchange of these particles does not cause any observable physical effects within a time interval Δt. An indistinguishability hypothesis is proposed for such particles, suggesting that two particles (or systems) with nearly the same degree of internal freedom will actually interchange under certain circumstances, thereby affecting the subsequent dynamics. This indistinguishability implies that, theoretically, it is possible to capture an elementary particle with extraordinarily large internal freedom by trading it for an isolated composite system of ordinary matter particles with almost the same total internal freedom as the large-freedom particle. Following this, the ordinary particles will instantly disperse into the environment, while the large-freedom particle will initially be captured and then gradually delocalized into the environment, an observable phenomenon. If this hypothesis is proven true in the future, it might provide a novel strategy for detecting dark matter particles.

We present a partition of quantum observables in an open quantum system which is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy which is consistent with the Laws of Thermodynamics.

In this paper, we introduce a novel controlled quantum communication protocol utilizing a quantum random walk involving one sender, one receiver, and multiple controllers. Inspired by classical random walk theory, quantum random walk serves as the foundation of our proposed protocol. With this protocol, we demonstrate the ability to transfer any n- dimensional quantum state to any party facilitated by any m number of controllers. Furthermore, any of the (m+1) individuals has the freedom to accept the role of the receiver. Rigorous testing of the protocol’s performance is conducted through quantum state tomography. We have run different variations of the circuits in IBMQ QASM simulator. Additionally, we explore the effectiveness of a weak measurement-based protocol designed to mitigate amplitude-damping noise’s detrimental effects on quantum states. By analyzing fidelity versus amplitude damping noise-strength plots for scenarios with and without the weak measurement protocol, we provide valuable insights into its protective capabilities across various levels of noise. These find- ings illuminate the protocol’s potential applications in quantum information processing

Some time ago, Kobayashi et al. experimentally studied the so-called Lee-Naughton-Lebed's (LNL) angular effect in strong electric fields [K. Kobayashi, M. Saito, E. Omichi, and T. Osada, Phys. Rev. Lett. \textbf{96}, 126601 (2006)]. They found that strong electric fields split the LNL conductivity maxima in $\alpha$-(ET)$_2$-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this Letter, for the first time we suggest quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the obtained by us approximate theoretical formula coincides with the hypothetical one and well describes the above mentioned experiments.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

Entanglement is one of the most striking features in quantum systems. Today, quantum entanglement plays a vital role in quantum technology, the non-classical correlation of quantum entanglement is an important resource for quantum communication and quantum computing. Entanglement can be divided into two categories: between multi-particle systems and between various degrees of freedom in a single-particle system (intraparticle entangled states). This work first analogized the distinctions and connections between two kinds of entangled states. Then it designed three types of entanglement-swapping methods based on Bell state joint measurement, cross-Kerr medium, and linear optical elements for intraparticle entangled states by analogizing the entanglement swapping between multiple particles. Intraparticle entanglement swapping can be applied in super quantum dense encoding, quantum information transmission, and quantum teleportation. This work is beneficial for promoting the development of quantum information technologies.

Despite their Nobel prize-winning empirical confirmation, the interpretation of the Bell inequality remains controversial. By carefully analyzing Bell's work on nonlocality, we show how the correct appreciation of Bell's rationale calls for reformulating a widespread argument on quantum nonlocality, yielding a more consistent formulation of the problem. We delve into a formal proof of quantum mechanics' violation of local causality strikingly overlooked in favor of less appropriate arguments. For completeness, we also mention a few alternatives that may rationally justify considering quantum mechanics as a local theory.

We humans are natural-born engineers. As such, we model after machines not only isolated, naturally occurring systems, but also the basic laws of physics, sharing with machines a local-evolution-of-state `grammar'. However, previous work by the author casts doubt upon this mechanistic paradigm, suggesting that it is to blame for the stubbornness of many open problems in physics. Simple experiments are therefore proposed to identify `non-machines'. In one experiment, `non mechanistic correlations' in the spirit of Bell are sought in a pair of separated but previously coupled (macroscopic) chaotic systems. In another it is tested whether chaotic systems could fuzzily `remember their future' in the sense that a future binary perturbation applied to them could be inferred from their present behavior with probability>1/2. Chaotic systems are chosen as candidates because the long-time application of their (deterministic) mechanistic description is conceptually groundless: All scales are significant and mutually coupled in that regime, down to scales governed by QM, yet the quantum-classical transition remains inexplicable---if only due to the measurement problem. Similarly for non-deterministic chaotic systems, modeled as such purely for defying a short-time deterministic mechanistic description. Should a non mechanistic signature be found in such simple systems, the implications for science as a whole and life sciences in particular cannot be overstated.

This research review explores the synthesis of graphene quantum dots (GQDs) from biowaste for supercapacitor applications, driven by the need for sustainable and efficient energy storage technologies. GQDs, with their unique properties like high surface area and excellent conductivity, hold promise for enhancing supercapacitor performance. Various synthesis methods, including hydrothermal/solvothermal processes, chemical exfoliation, carbonization/pyrolysis, and microwave-assisted synthesis, are discussed alongside characterization techniques to evaluate GQD properties. Biowaste-derived GQDs demonstrate significant potential by improving specific capacitance and cycling stability in supercapacitor electrodes. Challenges such as scalability and material purity are identified, with future directions focusing on enhancing energy density, cycle life, and cost-effectiveness to propel the adoption of biowaste-derived GQDs in commercial energy storage applications.

A deterministic quantum mechanics theory is presented in a series of papers starting with the present one. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle- wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is shown to be consistent with the proposed deterministic quantum mechanics theory. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines, as well as the fine structure constant emerge directly from the solution of the equations governing theproposed deterministic quantum mechanics presented in Part II of these series of papers.

The interaction of matter when separated by a distance is a fundamental question, whether such interactions occur through instantaneous action at a distance or retarded interaction (principle of locality)? While the mainstream consensus favors the principle of locality, instantaneous action at a distance offers certain advantages. Previously, instantaneous action at a distance has been viewed as an appearance or representation from specific gauge choices of electromagnetic potentials (retarded). In this paper, we propose a novel approach that combines Weber’s electrodynamics with the concept of vacuum polarization to explore a new possible connection between the two viewpoints: instantaneous action at a distance and the locality principle. This new approach aligns with the observation of locality in signal/energy propagation while retaining the notion of instantaneous action at a distance.

Inspired by works of W. H. Zurek and others, a mathematical, physical theory, entirely within a quantum mechanical formalism, is proposed for cognitive processes in terms of an abstract Hilbert-space for the conscious state that is an exact replica of the Hilbert-space for the neuronic physical state. Thus, any actual state of consciousness arises by its formal alignment (identification) with some-one in the set of the neuronic states, with the latter undergoing perpetual changes in the wake of life-long experiences. It is posited that these changes become expressed by an increase in the number of ordered, coherent neuronic states at the expense of the pre-ordinal random neuronic states. Changes, transitions between states are induced by a Gorini-Kossakowski-Sudarshan-Lindblad formalism, which is also instrumental in the effect of the conscious state on bodily actions. The paradigmatic findings of R.N. Shepard (1958 - 2011) and of S. Sternberg (1966 - 2016) for long- and short-term recalls are interpreted within the model.

This is the second paper in a series introducing a deterministic quantum mechanics theory that is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. The first paper in this series demonstrated how causality, physical reality, and determinism are restored and concerns that were raised by results from the current mainstream statistical quantum theory were explained in simple form. The meaning of particle-wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another and does that at irregular time intervals, the natural collapse of the wave function as part of the solution, as well as consistency with the phenomenon of entanglement were some of the results that emerged from the proposed deterministic quantum mechanics theory. While the first paper presented overwhelming evidence of the latter, the present paper is the first to produce actual solutions that are consistent with current mainstream quantum theory as well as with classical physics. Analytical solutions are presented via a linear stability method. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines, as well as the fine structure constant emerge directly from the solution of the equations governing the proposed deterministic quantum mechanics. Recommended follow-up solutions as well as generalizations are being presented at the end of the paper.

A two-qubit Hamiltonian model exhibiting an SU(2) symmetry is considered. The related dynamical problem results to be then exactly solvable both in the time-independent and in the time-dependent case. Basing on the formal, general form of the related time evolution operator, the time-dependence of the level of entanglement of some initial conditions is studied within both the Rabi and the Landau-Majorana-Stückelber-Zener scenarios.

Quantum computing is tipped to lead the future of global technological progress. However, the obstacles related to quantum software development are an actual challenge to overcome. In this scenario, this work presents an implementation of the quantum search algorithm in Atos Quantum Assembly Language (AQASM) using the quantum software stack my Quantum Learning Machine (myQLM). We present the creation of a virtual quantum processor whose configurable architecture allows the analysis of induced quantum noise effects on the quantum algorithms. The codes are available throughout the manuscript so that readers can replicate them and apply the methods discussed in this article to solve their own quantum computing projects. The presented results are consistent with theoretical predictions and demonstrate that AQASM and myQLM are powerful tools for building, implementing, and simulating quantum hardware.

The electron of spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory, an intuitive form of the fermion still remains lacking and it is often described by the so-called Dirac belt trick. In this novel undertaking, the electron is examined within the boundary posed by a recently proposed MP model of a hydrogen atom into 4D space-time. Its transformation to Dirac fermion appears consistent with Dirac belt trick, quantum mechanics and Lie group with gravity considered to be a classical force for an irreducible spinor field. These outcomes are compatible with Dirac field theory and its associated features like wave function collapse, quantized Hamiltonian, non-relativistic wave function, Weyl spinor, Lorentz transformation and Feynman diagrams. The model though speculative, it could become important towards defining the fundamental state of matter subject to further examinations.

Models of quantum measurements are presented, including observers subject to the laws of quantum mechanics. Observers perform multiple measurements in an attempt to disprove the collapse hypothesis. It is shown that under reasonable assumptions the effort cannot succeed. Under a unitary evolution the end state is a correlation between the result of the first measurement and the result(s) of the others, consistent with the observer's collapse hypothesis. The observer may conclude that the laws of nature include a non-unitary collapse mechanism, even if one does not actually exist. Discard of information is the crucial factor which distinguishes entanglement from measurement.

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave-particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave-particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This article reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave-particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This article constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation.

Recent efforts to conceptually design a technologically meaningful electromagnetic retarded engine indicated that this can only be done using the immense charge and current densities which exist in the atomic scale. However, this scale cannot be described by Newtonian physics, and only a quantum description will suffice to describe the dynamics of an electron on this scale properly. Here we study the retarded field quantum engine and highlight the differences between the quantum and the classical retarded engines.

A challenge in building large-scale superconducting quantum processors is the precise control and manipulation of the qubit state. However, the crosstalk between the microwave control lines impedes the parallel execution of high-fidelity digital and analog quantum operations. Here, we propose and demonstrate a universal compensation protocol for calibrating the microwave signal crosstalk. We also introduce amplified error sequences to optimize the accuracy. Furthermore, we show a definitive improvement in parallel gate operations with crosstalk cancellation, demonstrating the technique's effectiveness. This work paves the way for superconducting hardware that features automated calibration of microwave crosstalk, leading to enhanced fidelities in multiqubit circuits.

Quantum nonlocality represents correlation properties between subsystems of a composite quantum system, usually including the four types: Bell nonlocality, steerability, entanglement, and quantum correlation (quantum discord). Given a basis $e_{AB}=\{|e_{ij}\>\}_{i\in[d_A],j\in[d_B]}$ for the Hilbert space $\H_A\otimes \H_B$ of a bipartite system $AB$, a density operator $\rho^{AB}$ (quantum state) of $AB$ can be represented as a $d_Ad_B\times d_Ad_B$ matrix $\hat{\rho}_{e_{AB}}=[\]$, called the density matrix of a density operator $\rho^{AB}$. A natural question is what is the relationship between the quantum nonlocality of a density operator $\rho^{AB}$ and its corresponding density matrix $\hat{\rho}_{e_{AB}}$? In this work, we discuss the relationships between quantum locality and basis, and prove that one type of quantum locality of density operators and that of their density matrices under a basis are the same if and only if the chosen basis is the tensor product of the bases of subsystems. Consequently, different bases define different quantum nonlocality density operators.

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc…Using the PBN, many formulas, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman-Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential Applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

Quantum Rayleigh scattering of single photons rules out coincident detections of the originally entangled, paired photons Correlations between independent states of qubits can easily outperform those calculated with entangled photons. The quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed.

The relationship between physics and information processing is a topic of great significance in the realm of science and technology. The laws of physics, which govern the behavior of matter and energy, also have a profound influence on the way information is processed and utilized. While the mathematics governing information processing has not extensively utilized the laws of physics, it is evident that there is potential for these laws to play a more significant role, particularly in the context of quantum systems. based on the equivalence between information and energy, we can explore how other laws of physics can effectively contribute to more efficient and advanced information processing techniques. This research sheds light on the interconnectedness of physics and information processing, and its findings have the potential to significantly enhance our ability to process information, particularly in cutting-edge quantum systems. By recognizing and leveraging the influence of physics, we can pave the way for further advancements in information processing technologies.

Silica on Silicon is a major optical integration platform, while the emergent class of integrated Laser written circuits' platform offers additionally high customizability, and flexibility for rapid prototyping. However, the inherent waveguides' low core/cladding refractive index contrast characteristic compared to other photonic platforms in silicon or silicon nitride, sets serious limitations for on-chip efficient coupling with single photon emitters, like semiconductor nanowires with quantum dots limiting the applications in quantum computing. A new light coupling scheme proposed here overcomes this limitation providing means for light coupling >50%. The scheme is based on the incorporation of an optical microsphere between the nanowire and the waveguide, properly optimized and arranged in terms of: size, refractive index, distance of microsphere between nanowire and waveguide. Upon suitable design of the optical arrangement, the photonic nanojet emitted by the illuminated microsphere excites efficiently the guided eigenmodes of the input channel waveguide, thus launching light with high coupling efficiency. The method is tolerant in displacements, misalignments, and imperfections and is fabricationally feasible by current state of the art techniques. The proposed method enables the on-chip multiple single photon emitters' integration thus allowing the development of highly customizable and scalable quantum photonic integrated circuits for quantum computing.

Time evolution of the quantum correlation of the hybrid qubit-qutrit system in multilocal and global dephasing under the effect of a classical noises environment is presented. We considered the qutrit in z direction and the qubit x direction. In addition, our system presents two configurations: the different and the common environment and our discussion involves three types of noises: A Static Noise (SN), Random Telegraph Noise (RTN) and Ornstein- Uhlenbeck noise (OU). By using the density matrix approach to determine the evolution of the state of the system, the found that the static noise is fatal for the quantum entanglement, the quantum correlation and for RTN and OU noises the quantum entanglement, the quantum correlation decreases monotonically with a sufficiently long time. Therefore, we can say that, entanglement and the quantum correlation are more robust to the noise precisely those Random telegraph noise and Ornstein-Uhlenbeck noise.

Quantum cryptography revolutionizes secure information transfer, providing defense against both quantum and classical computational attacks. The primary challenge in extending the reach of quantum communication comes from the exponential decay of signals over long distances. Addressing this challenge, we have developed Quantum-protected Control-based Key Distribution (QCKD), overcoming transmission range limitations by monitoring signal leakages and rendering leaked quantum states significantly non-orthogonal. This paper reports on the experiments with the QCKD, conducted over a 1,707 km fiber line. We demonstrate advancements in critical components of the protocol, showing its remarkable scalability and adaptability for extended distances and multi-user configurations.

We changed the symmetry of the Weak Force from SU(2) to the quaternion group $Q_8$, and found that spin spacetime separates into two complementary spaces: a spin polarization spacetime of even parity states, and a spin coherence space, in the $S^3$ hypersphere, of odd parity coherent states. Under the quaternion group, spin is a boson of spin 1 in free flight and a fermion of spin $\frac{1}{2}$ when measured. It immediately follows that neutrinos are not needed to balance spin and conserve energy in beta decay. Additionally, we find the boson electrons emitted in beta decay are odd to parity, leading to parity conservation even though the observed beta distribution is asymmetrical.

Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.

The question of what generates conscious experience has mesmerized thinkers since the dawn of humanity, yet its origins remain a mystery. The topic of consciousness has gained traction in recent years, thanks to the development of large language models that now arguably pass the Turing test, an operational test for intelligence. However, intelligence and consciousness are not related in obvious ways, as anyone who suffers from a bad toothache can attest - pain generates intense feelings and absorbs all our conscious awareness yet nothing particularly intelligent is going on. Still, in the hard sciences, this topic is frequently met with skepticism because to date no protocol to measure the content or intensity of conscious experiences in an observer-independent manner has been agreed upon. Here we present a novel proposal: Conscious experience arises whenever a quantum mechanical superposition forms. Our proposal has several implications: First, it suggests that the structure of the superposition determines the qualia of the experience. Second, quantum entanglement naturally solves the binding problem, ensuring the unity of phenomenal experience. Finally, a moment of agency may coincide with the formation of a superposition state. We outline a research program to experimentally test our conjecture via a sequence of quantum biology experiments. Applying these ideas opens up the possibility of expanding human experience through brain-quantum computer interfaces.

The design and operation of quantum networks are both decisive in the current push towards a global quantum internet. Although space-enabled quantum connectivity has already been identified as a beneficial candidate for long-range quantum channels for over two decades, the architecture of a hybrid space-ground network is still a work in progress. Here, we propose an analysis of such a network based on a best-path approach, where either fiber- or satellite-based elementary links can be concatenated to form a repeater chain. The network consisting of quantum information processing nodes, equipped with both ground and space connections, is mapped into a graph structure, where edge weights represent the achievable secret key rates, chosen as the figure of merit for the network analysis. A weight minimization algorithm allows identifying the best path dynamically, i.e., as the weather conditions, stray light radiance, and satellite orbital position changes. From the results we conclude that satellite links will play a significant role on the future large-scale quantum internet, and both a constellation of satellites and significant advances in filtering technology are required to fulfill continuous coverage.

The concept of {\it quantum ratio} emerged in the recent efforts to understand how Newton's equations appear for the center of mass (CM) of an isolated macroscopic body at finite body-temperatures, as the first approximation to quantum-mechanical equations. It is defined as $Q\equiv R_q/L_0$, where the quantum fluctuation range $R_q$ is the spatial extension of the pure-state CM wave function, whereas $L_0$ stands for the body's linear size (the space support of the internal, bound-state wave function). The two cases $R_q /L_0 \lesssim 1$ or $R_q/ L_0 \gg 1$, roughly correspond to the body's CM behaving classically or quantum mechanically, respectively. In the present note we elaborate more on this concept, illustrating it in several examples. An important notion following from introduction of the quantum ratio is that the elementary particles (thus the electron and the photon) are quantum mechanical, even when the environment-induced decoherence turns them into a mixed state. Decoherence and classical state should not be identified. This simple observation, further illustrationed by the consideration of a few atomic or molecular processes, may have significant implications on the way quantum mechanics works in biological systems.

Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.

Time and space are fundamental concepts for characterizing and understanding our world. Despite of continuous curiosity and extensive studies, the nature of time and space remains elusive, and the underlying quantum structure is unclear. Here we propose a molecular model based on energy space decomposition to incorporate time and space synthetically in a unified framework. In the proposed model, the multipole expansion of action mapped to energy modules in scalar, vector, and matrix forms, results in the generators of time, space, and a material framework, cloud. And the invariance of time, space and cloud transformation corresponds to the conservation of energy, momentum, and mass, respectively. The classification of energy modules reveals a periodicity of energy elements, which constructs a hierarchical world in a molecular framework with dynamics represented by energy transformations. Here the role of time and space could switch from each other, and motion is attributed to the coupling of particle with intermediate bosons, corresponding to energy transformations among different energy modules. The application on Bohr model demonstrates that this picture provides a consistent classical interpretation to the foundation of quantum mechanics, and suggests an atomic model for gravitation.

The Yang-Mills conjecture addresses the fundamental nature of the strong force, one of the four fundamental forces in nature, responsible for binding quarks together to form protons, neutrons, and other hadrons. It was proposed in the early 1950s, the Yang-Mills suggests a mathematical framework for describing the behaviours of gauge fields, which are the carriers of fundamental forces. In particular, it focuses on non-abelian gauge theories, where the gauge fields themselves interact with each other. The non-abelian aspect refers to the fact that the order of operations matters when combining these gauge transformations, leading to a more intricate structure compared to abelian theories. This conjecture posits the existence and significance of certain mathematical structures, known as Yang-Mills fields, which play a crucial role in the formulation of the Standard Model of particle physics. The Standard Model describes the electromagnetic, weak, and strong nuclear forces, as well as the elementary particles that constitute matter. Despite its foundational importance, proving the Yang-Mills conjecture has proven to be a formidable challenge. The conjecture is intimately connected to the concept of mass gap, which refers to the idea that the particles involved in the strong force interactions exhibit mass, in contrast to the photon in electromagnetism, which is massless. The successful resolution of the Yang-Mills conjecture is expected to deepen our understanding of the nature of particle physics and may provide insights into the unification of fundamental forces. In this regard we hereby provide solutions to solve Yang-Mills conjecture using the method of Self Information Entanglement and Quantum Information Transport Equations to elucidate the origin of Universe from Unperceivable Information called “Avyaktham” through the emergence of perceivable information “Vyaktham”. For the first time in the world we provided an empirically verifiable solution to the origin of emergence and existence of Universe based on the methods to predict the emergence using working model of clinical Ayurveda. It is computed that the value of mass gap mentioned in Yang-Mills conjecture is around mYM = mbit ≈ 1.06×10⁻⁴¹kg.

Sequential properties can violate Bell-type inequalities without direct influence on each other, but only if detected in pairs. This is demonstrated below with theoretical arguments, and with a straightforward toy model. Rotating arrows can have transient qualities that produce maximal Bell violations with predetermined values. Any non-signaling phenomenon (classical, or non-classical) can also be interpreted as local.

The Ising model, a cornerstone in the understanding of critical points, phase transitions, and magnetic systems, has been pivotal in advancing our knowledge of statistical physics. Although analytical solutions exist for the 1D and 2D Ising models, complexities rise significantly with the inclusion of external magnetic fields and in higher dimensions. Here, we demonstrate a novel quantum computational approach to simulate the 1D Ising model with basic quantum gates in the QISKIT(Python) that is both accessible to beginners and executable on personal computers, bypassing the need for advanced computational infrastructure. By initializing the system in a comprehensive superposition state, we effectively utilize quantum gates to replicate the intricate interactions between spins and external fields. This method offers a more intuitive and direct observational means of the system's evolution, distinguishing it from previous methodologies. Our results not only repeat all the physics behavior in the 1D Ising model but also showcase the expanding capabilities of quantum computing to tackle complex physical systems, promising advancements in both theoretical and applied physics.

For the first time in the world, we provided a phenomenologically verifiable proof for the validation of origin of universe and perceivable reality from the unperceivable information based on Ayurveda. We also provided the axiomatic definitions for the terminologies used to deliver the theoretical framework for the same based on Bharatheeya Knowledge Systems. The presented manuscript provides a corelation between quantum information transport and emergence of gunam “Laghu” and gunam “Guru”. We identified that this point of emergence can be considered as the origin point in the continuous process of generation of Perceivable Reality “Vyaktham” from Unperceivable Information “Avyaktham”. In this context we can consider the unperceivable information in “Avyaktham” as dark matter. So, we must develop methods like gunascopy or informationscopy to understand the types of information imbibed in the quantum matter of a dravyam to understand its original physico-chemical-biological and information state of the constituent matter. This is possible through the assessment of Dravya Guna aspects and panchabhootha tatwas of the dravyas. For the first time in the world, we have developed the method to derive all the gunas from “guru” and “Laghu” and calculated the mass of the finitie components of Nava Dravyas including Mann, Aatma, Kaal, Disha, Aakash, Vaayu, Agni, Jal and Prithvi from the quantum information emergence equation. We strongly believe that this work will open up new avenues to explore the frontiers of reality and universe through natural cognition. The solutions to the Yang-Mill conjecture is achieved by our team using the Quantum Information Emergence and Transport Equations. We proved that the information bounded in the quantum states of the constituent quantum matter of quantum particles will provide them positive masses, even though they travel at the speed of light. Based on the phenomenologically verifiable axioms proposed in this work, we proved that the space on the topologically invarient 2D Poincare Sphere which is equivalent to a 2D space without boundaries can facilitate the never-ending loop of continuous quantum information transport between “Avyaktham” and “Vyaktham”. So the information availabe in the constituent quantum states of “Avyaktham” is equal to the postiive mass of quantum systems travelling at the speed of light. In such condition all the mass of the quantum particles will be converted in to information bounded in the corresponding quantum states of the quantum matter. This complete conversion of mass of the quantumparticles into information will happen only at maximum entropy. Thus at maximum entropy the information which is self information entangled with its own quantum states in “Avyaktham” will have a positive mass equal to the mass gap proposed in the Yang-Mill conjecture.

Maximal quantum correlations of unity do not violate the CSHS-Bell inequalities because the remaining two correlations vanish. The probability of coincident detections should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed. © The Author 2023

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

By examining Planck's equation E=hν, one finds an analogy with accounting billing for electricity. Frequency and power have a physical dimension T-1, so one obtains an energy value accounted for over a time interval by multiplying them by this time interval. By investigating this analogy, one finds a surprising mistake in Planck's law for the frequency of black body radiation: confusion between two contexts, one for radiation power and one for a timeless energy density. One goes from one to the other by an accounting-type transformation: a multiplication by 4π/c or c/4π. Correcting this mistake makes a Planck constant h timeless, invalidating the photon definition and de Broglie’s wave-particle duality. Despite this mistake, one obtains the same value for the black body radiation; it goes unnoticed. Consequently, the Planck relation becomes P=hν, with the energy of a cycle equal to h, whatever the frequency. One can consider this cycle as a new photon, which behaves like a particle by its radiation pressure. Its energy-mass equivalence h=mɣc2 gives a mass of 4.134883524·10-15 eV, in the range referenced by the Particle Data Group. This correction of Planck's relation calls quantum physics into question.

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case to the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is just the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the Hilbert space version of the mathematics of partitions. Or putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic to information theory to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partitions are the ordered pairs of elements from the underlying set that are in different blocks of the partition. Logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run through the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

Engineering of quantum computers requires reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE) based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.

Using the projection evolution (PEv) approach, time can be included in the quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper we discuss the possibility of constructing a quantum clock, which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.

Plasmonic nanocomposites have the ability to enhance light-matter interaction due to the 1 plasmonic effects leading to promising potential applications. In this paper, we theoretically study the 2 group index of the silver nanoparticle-gold nanoparticle-quantum dot plasmonic hybrid system in 3 the optical region of the electromagnetic spectrum using the density matrix approach. The quantum 4 dot is considered to be a three-level atomic system of a lambda configuration, interacting with strong 5 control and weak probe fields. We find that the plasmonic hybrid system exhibits at near resonance a 6 strong switching between slow and fast light, which can be controlled by the inclination angle of the 7 gold nanoparticle and the size of the metals nanoparticles, in addition to the strength and detuning 8 of the control field. Thus, the silver nanoparticle-gold nanoparticle-quantum dot could potentially be 9 used in optoelectronic devices.10

We propose a correspondence between partition functions of ideal gases consisting of both bosons and fermions and algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sides sequences ℓ1(Z0). Such an approach allows us to interpret some combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence on ℓ1(Z0) induced by the supersymmetric polynomials, and semiring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semiring structures on this set and discuss their possible physical interpretations.

Plasmonic nanocomposites have the ability to enhance light-matter interaction due to the plasmonic effects leading to promising potential applications. In this paper, we theoretically study the group index of the silver nanoparticle-gold nanoparticle-quantum dot plasmonic hybrid system in the optical region of the electromagnetic spectrum using the density matrix approach. The quantum dot is considered to be a three-level atomic system of a lambda configuration, interacting with strong control and weak probe fields. We find that the plasmonic hybrid system exhibits at near resonance a strong switching between slow and fast light, which can be controlled by the inclination angle of the gold nanoparticle and the size of the metals nanoparticles, in addition to the strength and detuning of the control field. Thus, the silver nanoparticle-gold nanoparticle-quantum dot could potentially be used in optoelectronic devices.

The temperature-dependent intensities of the exciton (X) and biexciton (XX) peaks from single GaAs cone-shell quantum dots (QDs) are studied with micro photoluminescence (PL) at varied excitation power and QD size. The QDs are fabricated by filling of self-assembled nanoholes, which are drilled in an AlGaAs barrier by local droplet etching (LDE) during molecular beam epitaxy (MBE). This method allows the fabrication of strain-free QDs with sizes precisely controlled by the amount of material deposited for hole filling. Starting from the base temperature T = 3.2 K of the cryostat, single-dot PL measurements demonstrate a strong enhancement of the exciton emission up to a factor of five with increasing T. Both, the maximum exciton intensity and the temperature Tx,max of the maximum intensity depend on excitation power and dot size. At an elevated excitation power, Tx,max becomes larger than 30 K. This allows an operation using an inexpensive and compact Stirling cryocooler. Above Tx,max, the exciton intensity decreases strongly up to its disappearance. The experimental data are quantitatively reproduced by a model which considers the competing processes of exciton generation, annihilation, and recombination. Exciton generation in the QDs is given by the sum of direct excitation in the dot plus additional bulk excitons diffusing from the barrier layers into the dot. The thermally-driven bulk-exciton diffusion from the barriers causes the temperature enhancement of the exciton emission. Above Tx,max, the intensity decreases due to exciton annihilation processes. In comparison to the exciton, the biexciton intensity shows an only very weak enhancement, which is attributed to more efficient annihilation processes.

Many quantum devices signals are proportional to the number of the participating atoms that take part in the detection devices. Among these are optical magnetometers, atomic clocks, and atoms interferometers. One way to enhance the signal to noise ratio is to introduce atoms entanglement that increases the signal in a super-radiant like effect. An initial novel experiment to test the realization of atoms correlation is described here. A Cs optical magnetometer is used as a tool to test the operation of a cell-in-cavity laser and its characteristics. A vapor cell is inserted in-to an elongated external cavity of the pump laser in Littrow configuration. Higher atom polarization and reduced laser linewidth are obtained leading to better magnetometer sensitivity and signal-to-noise ratio. The Larmor frequency changes of the Free Induction Decay of optically pumped Cs atomic polarization in ambient earth magnetic field at room temperature is measured. Temporal changes in the magnetic field of less than 10 pT/Hz are measured. The first order dependence of the magnetic field on temperature and temperature gradients is eliminated, important in many practical applications. Single and gradiometric magnetometer con-figurations are presented.

True randomness is necessary for the security of any cryptographic protocol, including quantum key distribution (QKD). In QKD transceivers, randomness is supplied by one or more local private entropy sources of quantum origin, which can be either passive (e.g. a beam splitter) or active (e.g. an electronic quantum random number generator). In order to understand better the role of randomness in QKD we revisit the well-known "detector blinding" attack on BB84 QKD protocol, which utilizes strong light to achieve an undetectable and complete recovery of the secret key. We present two findings. First, we show that the detector blinding attack is in fact an attack on the receiver’s local entropy source. Second, based on this insight, we propose a modified receiver station and a statistical criterion which together enable robust detection of any bright-light attack and thus restore security.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

By utilizing a generalized version of the Madelung quantum-hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which a stable quantum state ultimately emerges in the presence of fluctuations induced by the noisy gravitational background. The model defines the conditions that give rise to a limited range of interaction for the quantum potential, allowing for the existence of coarse-grained classical descriptions at a macroscopic level. The theory uncovers the smallest attainable level of uncertainty in an open quantum system and examines its consistency with the localized behavior observed in large-scale classical systems. The research delves into connections and similarities with decoherence theory and the Copenhagen interpretation of quantum mechanics. Additionally, it assesses the potential consequences of wave function decay on the measurement of photon entanglement. To validate the proposed theory, an experiment involving entangled photons transmitted between detectors on the Moon and Mars is discussed. Finally, the findings of the theory are applied to the creation of larger Q-bits systems at elevated temperatures.

Recently, a paper was written to establish semi-structured complex numbers ℍ (a new number set invented to enable division by zero) as a useful mathematical tool providing novel results from its application in engineering and science. Whilst the paper was a milestone, the application of this number set to quantum and classical physics had not been fully explored. Consequently, the aim of this research was to use semi-structured complex numbers to develop a new mathematical model for the mass of an object and in course unite classical and quantum physics in a simple yet effective manner. As its major contributions this paper: (1) develops a new mathematical model for the mass of an object called the wave-mass function using De Broglie’s mass and frequency relation and semi-structured complex numbers; (2) uses the new wave-mass function to determine what happens to an object traveling at the speed of light; (3) derives a relation between Schrödinger’s wave function and the new wave-mass function; (4) derives a relation between Einstein’s Field Equation and the new wave-mass function; (5) uses the wave-mass function to combine Einstein’s Field Equation with Schrödinger’s wave function to form a new quantum gravity equation. These results and their applications provide a firm foundation to advance the number set ℍ as a useful mathematical tool.

Several mathematicians and physicists are working all over the globe to get a unified theory. However, most of them are discarding Einstein’s view at the very first step of their theories. This article provides a brief description about this. Also, on the basis of Koga’s theory we point out two reasons which might have caused Einstein’s failure to get a unified theory.

We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when one attempts to move from particle ontology into the realm of field ontology, i.e., when one transitions from mechanics to field theory framework. These issues need to be addressed, and problems solved, if one aims to expand the scope of applicability of the process matrix formalism, and therefore its usefulness. This is far from a trivial and straightforward endeavour, but rather a task for a whole future research programme.

We study the work fluctuations in ergotropic heat engines, namely two-strokes quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3 = U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs) which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.

The phenomenon of interference is a characteristic of all waves. This paper reviews the interference of classical waves and of matter waves in quantum mechanics. In quantum mechanics, there are two interference mechanisms between identical particles. One is that the de Broglie wavelengths of two interference waves are the same, which is called the equal wavelength interference mechanism. The other is that the wavelengths of interference waves can also be different, in which case there should be an exchange term in additional to the direction term in the wave function. There is a fixed phase difference between the two terms, which causes interference. This is called exchange effect interference mechanism. We propose an experiment, which is simpler to what has been done, to show the exchange effect interference. There is a special case where two interference waves can satisfy both the two mechanisms. We propose an experiment to discriminate that in this case which mechanism plays a role on earth.

By employing the stochastic extension of the Madelung quantum-hydrodynamic description within a discrete methodology, we establish a solution using the path integral approach to explore the progression of quantum states' superposition. This investigation aims to understand the eventual establishment of a stable end-state configuration amid the backdrop of gravitational background fluctuations. The model identifies the circumstances that lead to a limited range of interaction for the quantum potential, allowing for the emergence of sizeable, classically described macroscopic phenomena. The theory unveils the lowest achievable level of uncertainty in an open quantum system and investigate its congruence with the localized behaviors of macroscopic classical systems. The study examines agreements and differences with decoherence theory and the Copenhagen interpretation of quantum mechanics, and evaluates the impact of wave function decay on the measurement process.

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to currently not provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed `quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi bound (or resonance) states. When the system is prepared in one of such quasi bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and because of quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

Thermal fluctuations in two-dimensional (2D) isotropy systems at non zero finite temperatures can destroy the long-range (LR) magnetic order due to Mermin-Wanger theory. Interestingly, the magnetic anisotropy related to spin-orbit coupling (SOC) could stabilize magnetic order in 2D systems. Recently, 2D FexGeTe2 (3≤x≤7) with high curie temperature (TC), as a typical 2D van der Waals metallic ferromagnet, has not only made significant progress in synthetic methods and controlling ferromagnetism (FM), but also actively explored many device applications. In this Review, we introduce six experimental methods, ten ferromagnetic modulation strategies, and three spintronic devices of 2D FexGeTe2 materials. Overall, we have outlined the challenges and potential research directions in this field.

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

The famous Wigner’s friend experiment considers an observer – the friend– and a superobserver – Wigner– who treats the friend as a quantum system and her interaction with other quantum systems as unitary dynamics. This is at odds with the friend describing this interaction via collapse dynamics, if she interacts with the quantum system in a way that she would consider a measurement. These different descriptions constitute the Wigner’s friend paradox. Extended Wigner’s friend experiments combine the original thought experiment with non-locality setups. This allows for deriving local friendliness inequalities, similar to Bell’s theorem, which can be violated for certain extended Wigner’s friend scenarios. A Wigner’s friend paradox and the violation of local friendliness inequalities require that no classical record exists, which reveals the result the friend observed during her measurement. Otherwise Wigner agrees with his friend’s description and no local friendliness inequality can be violated. In this article, I introduce classical communication between Wigner and his friend and discuss its effects on the simple as well as extended Wigner’s friend experiments. By controlling the properties of a (quasi) classical communication channel between Wigner and the friend one can regulate how much outcome information about the friend’s measurement is revealed. This gives a smooth transition between the paradoxical description and the possibility of violating local friendliness inequalities, on the one hand, and the effectively collapsed case, on the other hand.

The notion of quantum-mechanics-free subsystem (QMFS) was introduced by Tsang and Caves in 2012. They showed that it is possible to design the dynamics of coupled quantum systems in such a way that one can construct a subsystem in which a given classical dynamics is realized, thus avoiding the measurement back-action of quantum mechanics. Although they mention that the Heisenberg picture equations of motion for QMFS was first proposed by Koopman in 1931 as a formulation of classical Hamiltonian dynamics in Hilbert space, in fact the connection between QMFS and Koopmann-von Neumann mechanics is deeper. Namely, quantum-mechanics-free subsystem is nothing but the realization of Sudarshan's perspective on the Koopman-von Neumann mechanics.

We present an analysis of recent experiments in femtoscopy by the STAR collaboration in terms of the protocol of entanglement witnessing involving purity measurements. The entanglement is between the charge and momentum degrees of freedom of pions and the state purity measurements ultimately rely on the bosonic nature of the detected pions. The pion experiment is intended to measure the size of nuclei and the distance between the nuclei involved, however it indirectly confirms that the states of dfferently charged pions are entangled through an entanglement witness based on the purity of various pionic states. The entangled state of pions can be modelled straightforwardly dynamically using a simple Hamiltonian. Quantum indistinguishability plays a key role in this analysis and we make comparison with the equivalent photonic experiments.

This paper discusses complexity theory, that is, the many theories that have been proposed for emergence of complexity from the underlying physics. Our aim is to identify which aspects have turned out to be the more fundamental ones as regards the emergence of biology, engineering, and digital computing, as opposed to those that are in fact more peripheral in these contexts. In the cases we consider, complexity arises via adaptive modular hierarchical structures that are open systems involving broken symmetries. Each emergent level is causally effective because of the meshing together of upwards and downwards causation that takes place consistently with the underlying physics. Various physical constraints limit the outcomes that can be achieved. The underlying issue concerns the origin of consciousness and agency given the basis of life in physics, which is structured starting from symmetries and variational principles with no trace of agency. A possible solution is to admit that consciousness is an irreducible emergent property of matter.

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as ‘cost oracle’ operations UC, which when combined with the standard Grover diffusion operator Us lead to high probabilities of measurement for states corresponding to the optimal and near optimal solutions. In order to achieve these probabilities, a single scalar parameter ps is required, which we show can be found through a variational quantum-classical hybrid approach.

The quantum Randi challenge is an invitation to violate Bell’s inequality with a programmable (transparent and reproducible) sequence of local events. This is widely perceived as impossible, given Bell’s Theorem. However, mathematical proofs can be correct without universal validity, as seen in the case of Euclidean geometry. Is Bell’s Locality Criterion inclusive enough to account for all the local phenomena? It is well known that Bell-type inequalities apply to jointly distributed variables, meaning that they hold for events that can be recorded at the same time. Yet, some physical qualities are mutually exclusive. They only become observable at different times. Accordingly, pairwise detections in a narrow window of coincidence – but not at the same exact time – allow for maximal Bell violations (S=4 for the CHSH inequality), without room for doubt about the local nature of the process.

Recent works have shown that collective single photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes emission from a completely symmetric state of N atoms, with a single excited atom prepared with a given phase, for instance imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining N−1 asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states.

The identification and physical interpretation of quantum correlations, more recently explored beyond entanglement, is not always a simple task. Two assumptions that, at least in principle, should lead to a relatively large dispersion for the observables of a quantum bipartite formed by systems I and II are to assume that; (a) all the possible observables describing the composite are potentially equally probable as outcomes of measurements; and (b) there cannot be concurrence (positive reinforcement) between any of the observables within a given system, meaning all their corresponding operators do not commute. The so-called EPR states are known to observe (a). Here we demonstrate in general terms that they also verify (b). As examples, we discuss three-level systems. Given the character of (a) and (b), one may expect the CHSH correlation for qubits to naturally violate its associated Bell’s inequality (i.e., it would yield values greater than 2) when applied to EPR states. Surprisingly, we show the CHSH contradicts such prediction. This finding emphasizes the subtleties of correlations in quantum mechanics, where the conceivable dispersive interdependence of EPR states observables results counterintuitively in a more limited range of values for the CHSH correlation, not surpassing the nonlocality threshold of 2.

The author’s opinion is that the negative energy solutions of the Dirac equation mean that a particle can be of negative kinetic energy (NKE) besides positive kinetic energy (PKE). We think that NKE particles are dark ones and NKE matter is dark matter. In our previous works, the dark matter theory of the NKE version and the dark energy theory that matched dark matter theory were put forth. In this work, we investigate the topics related to the metamorphosis of objects between PKE and NKE. We first evaluate the collosions between a PKE and a NKE particles. A scenario of accelerating PKE particles is raised. We put forth the cosmic dark radiation background and gravity potential background. In the universe, negative energy is predominating. In the observable universe, substances constitute stable PKE systems. The total energy of every such system is negative. We propose a mechanism that NKE substances combine into stable PKE systems. Macroscopically, NKE objects can constitute stable PKE astrophysical systems by means of gravity between them. Microscopically, NKE particles can combine into stable PKE systems by means of attractive interactions between them, say, Coulomb attraction. Currently, people think that there are four ingrediants in the universe: photons \Omega_R0, matter \Omega_M0, dark matter \Omega_DM, and dark energy \Omega_\lambda0. We analyze the order of the appearance of the four ingredients and conclude that qualitatively, their proportions should be \Omega_\lambda0 > \Omega_DM > \Omega_M0 > \Omega_R0.

PEDOT:PSS (polyethylene dioxythiophene:polystyrenesulfonate) is a commonly used hole injec-tion layer (HIL) in optoelectronic devices due to its high conductive properties and work function. However, the acidic and hygroscopic nature of PEDOT:PSS can be problematic for device stability over time. To address this issue, in this study, we have demonstrated the potential of an organic-inorganic hybrid HIL, by incorporating solution-processed WOx nanoparticles (WOx NPs) into the PEDOT:PSS mixture. This hybrid solution was found to have a superior hole transport ability and low Ohmic contact resistance, contributing to higher brightness (~62 000 cd m-2) and current efficiency (13.1 cd A-1) in the manufactured quantum-dot based light-emitting diodes (QLEDs). In addition, the resulting devices achieved a relative operational lifetime of 7,071 hours, or approxi-mately twice that of traditional QLEDs with PEDOT:PSS HILs. The proposed method is an un-complicated, reliable and low-cost way to achieve long operational lifetimes without sacrificing efficiency in optoelectronic devices.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e. with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e. the concept of neutron's (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle's dynamics from the quantum dynamics of the scatterer---a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, 'which-path detection' versus interference, von Neumann measurement, Week Values, etc.) new observable effects may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. 7