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.

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.

The rapid advancements and the merging of hybrid quantum-classical computing, artificial intelligence (AI), machine learning (ML), and deep learning (DL) pose a potentially unseen and significant threat to encryption that may impact Post-Quantum Cryptography (PQC) transition timelines. There is a direct hybrid quantum-classical computing threat on cryptography, and there is also a direct threat AI/ML on cryptography. However, the synergistic combination of these technologies presents known and unknown threats that need attention, focus action, and research. This paper reviews Grover's Adaptive Search (GAS), which combines Grover's Algorithm with adaptive techniques to optimize search further, potentially making it even more efficient for attacking encryption. This work also examines the quantum-accelerated Harrow-Hassidim-Lloyd (HHL) Algorithm, designed to solve systems of linear equations exponentially faster than classical algorithms in certain conditions. The HHL algorithm can solve some lattice-based problems, which have implications for lattice-based encryption. This technological confluence and its potential impact on cryptography and encryption necessitate a proactive and coordinated approach to developing and implementing quantum-resistant AI/ML cryptographic solutions. This paper reviews the technological confluence and its potential implications for classical cryptography and PQC transition timelines and calls for further research.

In this paper, the connections between quantum non-locality and permutation symmetries are explored. This includes two types of symmetries: permutation across a superposition and permutation of qubits in a quantum system. An algorithm is proposed for nding the separability class of a quantum state using a method based on factorizing an arbitrary multipartite state into possible partitions, cyclically permuting qubits of the vectors in a superposition to check which separability class it falls into and thereafter using a reduced density-matrix analysis of the system is proposed. For the case of mixed quantum states, conditions for separability are found in terms of the partial transposition of the density matrices of the quantum system. One of these conditions turns out to be the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separability is also proposed. The concept of permutation of qubits is shown to be useful in dening a new entanglement measure in the `engle'.

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.

We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a way that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly in performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT's internal quantum network

Tremendous progress has been witnessed in artificial intelligence within the domain of neural network backed deep learning systems and its applications. As we approach the post Moore’s Law era, the limit of semiconductor fabrication technology along with a rapid increase in data generation rates have lead to an impending growing challenge of tackling newer and more modern machine learning problems. In parallel, quantum computing has exhibited rapid development in recent years. Due to the potential of a quantum speedup, quantum based learning applications have become an area of significant interest, in hopes that we can leverage quantum systems to solve classical problems. In this work, we propose a quantum deep learning architecture; we demonstrate our quantum neural network architecture on tasks ranging from binary and multi-class classification to generative modelling. Powered by a modified quantum differentiation function along with a hybrid quantum-classic design, our architecture encodes the data with a reduced number of qubits and generates a quantum circuit, loading it onto a quantum platform where the model learns the optimal states iteratively. We conduct intensive experiments on both the local computing environment and IBM-Q quantum platform. The evaluation results demonstrate that our architecture is able to outperform Tensorflow-Quantum by up to 12.51% and 11.71% for a comparable classic deep neural network on the task of classification trained with the same network settings. Furthermore, our GAN architecture runs the discriminator and the generator purely on quantum hardware and utilizes the swap test on qubits to calculate the values of loss functions. In comparing our quantum GAN, we note our architecture is able to achieve similar performance with 98.5% reduction on the parameter set when compared to classical GANs. With the same number of parameters, additionally, QuGAN outperforms other quantum based GANs in the literature for up to 125.0% in terms of similarity between generated distributions and original data sets.

Quantum computing arrives. Preceded by Mādhava of Sangamagrāma and other Hindu mathematicians, around 1,500 CE, and our previous work, we show at least 4 quantum properties that are indeed universal in some number systems; here we use them to enable quantum computing. Using the sets B={0,1}, B^n, N, Z, Q, and Q*, one has +4 quantum properties that one can trust, as archetypes of easy communication to friends and foes, to ignoranti or cognoscenti, and for quantum consciousness. Therefore, this work applies to computer calculations, apps in cell phones, algebra, atoms, mathematics, physics, and the human mind.

Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than fully-connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multi-features in multidimensional data. In this paper, we present a multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multi-feature quantum convolution with average and Euclidean pooling and thus adapting the CNN structure to a variational quantum algorithm (VQA). Average pooling is based on the quantum Haar transform (QHT) and Euclidean pooling is based on partial quantum measurement. The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results showed favorable characteristics of our proposed techniques compared to existing work with respect to a number of quantitative metrics such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.

“Non-Locality is most naturally incorporated into a theory in which there is a special frame of reference. One possible candidate for this special frame of reference is the one in which the Cosmic Microwave Background (CMB) is isotropic. However, other than the fact that a realistic interpretation of quantum mechanics requires a preferred frame and the CMB provides us with one, there is no readily apparent reason why the two should be linked” (L. Hardy). Starting from this remark we first argue that, given the present view of the vacuum, the basic tenets of Quantum Field Theory cannot guarantee that Einstein Special Relativity, with no preferred frame, is the physically realized version of relativity. Then, to try to understand the nature of the hypothetical preferred Σ−frame, we consider the so called ether-drift experiments, those precise optical measurements that try to detect in laboratory a small angular dependence of the two-way velocity of light and then to correlate this angular dependence with the direct CMB observations with satellites in space. By considering all experiments performed so far, from Michelson-Morley to the present experiments with optical resonators, and analyzing the small observed residuals in a modern theoretical framework, the long sought Σ− frame tight to the CMB naturally emerges. Finally, if quantum non-locality reflects some effect propagating at vastly superluminal speed vQI→∞, its ultimate origin could be hidden somewhere in the infinite speed cs→∞ of vacuum density fluctuations.

Inferring algorithmic structure in data is essential for discovering causal generative models. In this research, we present a quantum computing framework using the circuit model, for estimating algorithmic information metrics. The canonical computation model of the Turing machine is restricted in time and space resources, to make the target metrics computable under realistic assumptions. The universal prior distribution for the automata is obtained as a quantum superposition, which is further conditioned to estimate the metrics. Specific cases are explored where the quantum implementation offers polynomial advantage, in contrast to an indispensable exhaustive enumeration in the corresponding classical case. The unstructured output data and the computational irreducibility of Turing machines make this algorithm impossible to approximate using heuristics. Thus, exploring the space of program-output relations is one of the most promising problems for demonstrating quantum supremacy using Grover search that cannot be dequantized. Experimental use cases for quantum acceleration are developed for self-replicating programs and algorithmic complexity of short strings. With quantum computing hardware rapidly attaining technological maturity, we discuss how this framework will have significant advantage for various genomics applications in meta-biology, phylogenetic tree analysis, protein-protein interaction mapping and synthetic biology. This is the first time experimental algorithmic information theory is implemented using quantum computation. Our implementation on the Qiskit quantum programming platform is copy-left and can be found on https://github.com/Advanced-Research-Centre/QPULBA

Moore’s law will cease to be relevant once transistors are the size of electrons. Once this occurs, we will no longer be able to use silicon for technological advancement. However, breakthroughs will continue in the form of a sixth paradigm: a 3D molecular computing model such as quantum comput- ing. Some of the promising areas of quantum computing researched in this study are (i) algorithmic advancements - such as Shor’s, Grover’s, error correction, fault tolerance and other new algorithms; (ii) hardware - such as the quantum system architecture, circuit models, entanglement, superposition and no-cloning qubits; (iii) market segments - such as finance, healthcare, and chemistry; (iv) the supremacy established over classical computing; and (v) areas of applicability. Significant progress has been made in these areas in recent decades, and they have garnered immense interest, attention and the funding required to make good progress.

The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by the 2022 Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview.

Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in quantum mechanics the standard view is that particles of the same kind (``identical particles'') are completely indistinguishable from each other. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of ``particle'' in ordinary language and in classical physical theory, but also with how this term is used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by ``particles'' in the classical limit of quantum mechanics. Elaborating on earlier work, we here discuss an alternative to the standard view that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory concerning the question of when identical particles can be considered to be entangled.

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

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

1) We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time $t$. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time $t_0$ under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove that both these situations cannot arise under ordinary circumstances and thus measurement processes cannot be modelled by physical Hamiltonians.

In 1935 Einstein, Podolsky, and Rosen (EPR) studied general entangled states in the two photon experiment and pointed out the contradiction between local realism and the completeness of quantum mechanism. Most of the EPR experiments in recent years are based on the detection of polarization correlations of optical photons between spatially separated photon channels, some of which are split and directed to two spatially separated Michelson interferometers. Later, the two arms of Michelson interferometers are replaced by dual-channel Fabry-Perot (F-P) interferometry enabling precise analysis of the energy-time entanglement between a pair of photons. On the other hand, F-P type detectors on gravitational radiation have caught dozens of gravitational wave (GW) events successfully. This paper proposes a combined experiment of EPR and GW, exhibiting whether the coincident rate of EPR is modulated by GW induced change of cavity length or not. Such an experiment could test the coupling of quantum mechanics and general relativity for the first time, and be a useful tool to explore the nature of quantum gravity.

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

Quantum Computation, in the gate array version, uses logical gates adopting convenient forms for computational algorithms based on those of classical computation. There, two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite, their design depends on specific quantum systems and physical interactions involved, exacerbating the dynamics analysis. Predictable and controllable manipulation should be addressed to control the quantum states, but resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in SU(2^2d) for 2d-partite two-level systems into 2^2d-1 SU(2) quantum subsystems. Decomposition lets to set control procedures, to generate large entangled states and to design specialized dedicated quantum gates. There, easy and traditional operations proposed by quantum computation are recovered for more complex and large systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the generalized Bell states basis. It could be understood as a momentary splitting of the 2d information channels into 2^2d-1 pairs of 2 level quantum information subsystems and a settlement of the quantum information manipulation free of the imposed restrictions by the underlying physical system.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M3. More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group PSL(2, Z) correspond to d-fold M3- coverings over the trefoil knot. In this paper, one also investigates quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M3’s obtained from Dehn fillings are explored.

A single qubit may be represented on the Bloch sphere or similarly on the $3$-sphere $S^3$. Our goal is to dress this correspondence by converting the language of universal quantum computing (uqc) to that of $3$-manifolds. A magic state and the Pauli group acting on it define a model of uqc as a POVM that one recognizes to be a $3$-manifold $M^3$. E. g., the $d$-dimensional POVMs defined from subgroups of finite index of the modular group $PSL(2,\mathbb{Z})$ correspond to $d$-fold $M^3$- coverings over the trefoil knot. In this paper, one also investigates quantum information on a few \lq universal' knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on SnapPy. Further connections between POVMs based uqc and $M^3$'s obtained from Dehn fillings are explored.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

We derive a quantum speed limit for unitary evolution for the case of mixed quantum states using the stronger uncertainty relation for mixed quantum states. This bound can be optimized over different choices of Hermitian operators for a better bound. We illustrate this with some examples and show its better performance with respect to three existing bounds for mixed quantum states.

In this work, we present some results related with the issue of the Loop Quantum Black Holes (LQBH) thermodynamics by the use of the tunneling radiation formalism. The information loss paradox is also discussed in this context, where we have considered the influence of back reaction effects.

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.

The recent Google’s claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr’s principle of complementarity¹ (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd’s calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n). Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.

The shortage of quantum computers, and their current state of development, constraints research in many fields that could benefit from quantum computing. Although the work of a quantum computer can be simulated with classical computing, personal computers take so long to run quantum experiments that they are not very useful for the progress of research. This manuscript presents an open quantum computing simulation platform that enables quantum computing researchers to have access to high performance simulations. This platform, called QUTE, relies on a supercomputer powerful enough to simulate general purpose quantum circuits of up to 38 qubits, and even more under particular simulations. This manuscript describes in-depth the characteristics of the QUTE platform and the results achieved in certain classical experiments in this field, which would give readers an accurate idea of the system capabilities.

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in [1] by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

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.

In this paper, I propose new models of quantum information processing using the exchange interaction in physical systems. The partial SWAP operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence-free subspaces. Given the non-commutativity of these operators (for adjacent operators operating on a common qubit), a number of quantum states and entanglement patters can be obtained. This zoo of states can be classified, due to the parity constraints and permutation symmetry of the states, into invariant subspaces that are used for the definition of some of the applications in this paper.

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.

There is a formal analogy between the evolution of the universe, when this is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e. evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances.

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

Two opposed p–n diodes are connected with another junction that causes cancellation of the electric field in the depletion layer of each diode by the field of the other diode. This derived quantum diode is called the A system. Another dual diode, constructed by the same process but with the p- and n-types positioned as duality, called the B system. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts a momentum (i.e., a wave number) to the carriers in the absence of any internal voltage. Thus, a superconducting bias current density appears without the need for cooling. The reappearances of electron–hole pairs on the junction surfaces are assumed to be described by entire wavefunctions normalized by the band gap. Based on the bias superconducting current, NOT and NAND gates were constructed from the quantum diode systems. Numerical calculations revealed that the constant phases of the entire wavefunctions of the p-and n-types converged. Accordingly, it was clarified that Bose–Einstein condensation and the Meissner effect (described by the London equation) occurred in the quantum diode systems. Moreover, the systems exhibited rectification characteristics and a switching speed of the order of 10^-14 s. Combining this switching property with the large bias superconducting current (of the order of several V), we developed NOT and NAND gates with direct quantum correlations among many qubits, which are unaffected by random and thermal noises. These gates have memorization and initialization properties and are compatible with existing and accumulating programing algorithms. Moreover, when harvesting a divergent current output from these systems, the bias superconducting current and memorization property preserve the formed quantum correlations.

It is impossible to fully grasp reality and the universe without a sound understanding of quantum science, i.e. theory. The aim of this paper is twofold, namely first presenting what quantum information processing consists of, and then consequently discussing the implications of quantum science to the understanding of reality. I shall claim that the world is fully quantum, and the classical world is but a limit case of the quantum world. The crux of the argument is that quantum information can be taken as a living phenomenon. Quantum information processing (QIP) has been mainly the subject of computational approaches (Cooper and Hodges, 2016). Here we take it as the way in which information allows for a non-dualistic explanation of the world. In this sense, quantum information processing consists in understanding how entanglement stands as the ground for a coherent reality yet highly dynamical, vibrant and vivid. Information, I argue, is a living phenomenon that creates itself out of nothing. Quantum information is a relational view of entities, systems, phenomena, and events (Auletta, 2005).

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.

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.

Quantum mechanics is often described as irreducibly non-local. A tacit element of this picture is the assumption that one and the same sub-ensemble of quanta is post-selected in every measurement combination of a Bell test. Yet, this expectation was recently shown to be formally inconsistent with quantum theory (Cetto et al., 2020) and even to be experimentally falsifiable (Mardari 2021). The need to make sense of this development motivated a rigorous conceptual analysis of quantum non-locality, especially as it relates to the basic principles of quantum mechanics. The simple conclusion is that quantum theory and quantum non-locality are fundamentally incompatible. This is not a loophole around the predictions of quantum mechanics, but rather an insight into the essential conditions that make them accurate.

Controllable, quantum-strong correlations of polarization states can be implemented with multi-photon independent states. Polarization-based photonic quantum correlations can be traced back to the overlap of the polarization Stokes vectors on the Poincaré sphere between two polarization filters. The quantum Rayleigh scattering prevents a single photon from propagating in a straight line inside a dielectric medium, and it also provides a mechanism for the projective measurement of polarization. Complexities associated with single-photon sources and detectors can be eliminated because the quantum Rayleigh scattering in a dielectric medium destroys entangled photons. Entanglement-free, identical sources and processing devices give rise to correlations rather than these being caused by “quantum nonlocality”. These analytic developments were prompted by the vanishing expectation values of the Pauli spin vector for a single photon of maximally entangled photonic Bell states.

Quantum image representation is a widely researched area of quantum computing. Currently developed methods use angle parameter of the rotation gate (e.g., the FRQI method), sequences of qubits (ex. NEQR method) or phase shift (ex. LPIQE method) for storing color information of pixels. All of those methods are affected by decoherence and other classical and quantum noise, which is an inseparable part of quantum computing in a NISQ (Noisy Intermediate Scale Quantum) era. These all phenomenons influence the measurements, its probability distribution over the measurement basis and, as the result, makes the extracted images not even similar to those, which was stored in quantum computers. Since this process is, in its foundation, quantum as well, the computational reversal of this process is possible. There are a lot of methods for error correction, mitigation and reduction, but all of them use quantum computer time, or additional qubits to achieve desired result. We report a successful use of the Generative Adversarial Network tuned for image-to-image translation in conjunction with PDU method, for error reduction in images encoded using LIPQE (Local Phase Image Quantum Encoding) method.

The recently proposed and logically developed paradigm of deep genetical affinity of scientific terms "energy-entropy-information" harmonizes classical and quantum physics with general and special theories of relativity. For the first time in engineering practice, a complex vector-tensor-matrix description of gravitational, thermal and electromagnetic fields in ideal solid, liquid and gaseous media was performed analytically and without preliminary measurements. The basic set of fundamental quantum constants of the standard physical model has been computed with an extreme precision of 1/10^64, which is a natural limit arising due to elementary recursive arithmetic and elementary functional analysis in digital notation.

The paper describes a model of subjective goal-oriented semantics extending standard "view-from-nowhere" approach. Generalization is achieved by using a spherical vector structure essentially supplementing the classical bit with circular dimension, organizing contexts according to their subjective causal ordering. This structure, known in quantum theory as qubit, is shown to be universal representation of contextual-situated meaning at the core of human cognition. Subjective semantic dimension, inferred from fundamental oscillation dynamics, is discretized to six process-stage prototypes expressed in common language. Predicted process-semantic map of natural language terms is confirmed by the open-source word2vec data.

Quantum amplitude estimation is a numerical integration technique and a candidate for the first operationally used quantum algorithm providing a quantum advantage in the NISQ era. Its main metric is the generated Fisher information per second, as it describes the accuracy of the numerical integration. The development of this metric can be coupled to the quantum volume of the used quantum processor with a phenomenological noise model. Since the increase of the quantum volume seems to follow an exponential pattern, insight in the integration power of quantum amplitude estimation for the upcoming years can be obtained. This shows that quantum amplitude estimation as a numerical integration technique will not provide an advantage for functions without significant improvements to the connectivity, reliability and speed of quantum processors. Beyond that, this method may be used the estimate the development of many more NISQ era algorithms.

Practical entanglement distillation is a critical component in quantum information theory. Entanglement distillation is often utilized for designing quantum computer networks and quantum repeaters. The practical entanglement distillation problem is formulated as a bilevel optimization problem. A fuzzy formulation is introduced to estimate the quantum state (density matrix) from pseudo-likelihood functions (i.e., quantum state tomography). A scale-independent relationship between fuzzy relations in terms of the pseudo-likelihood functions is obtained. The entanglement distillation optimization problem was solved using the combined coupled map lattice and dual annealing approach. Comparative analysis of the results is then conducted against a standard dual annealing algorithmic implementation.

By expressing the Schrödinger wave function in the form $\psi =R{e}^{iS/\hslash }$ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., $V_Q=-\frac{{\hslash }^2}{2m}\frac{{\nabla }^{2}R}{R}$ , we have obtained a spin potential $V_S=-\frac{S{\nabla }^{2}S}{m}$ that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $m{c}^2$ with an internal frequency of $2m{c}^2/\hslash$ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

In this letter, it is proposed that cryogenic quantum bits could operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated and the sensitivity of quantum bit frequency and anharmonicty with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process could reveal the expected properties, thus putting the context of quantum computing hardware into new perspectives.

Quantum correlations, especially time correlations, are crucial in ghost imaging in order to significantly reduce the background noise on the one hand while increasing the imaging resolution. Moreover, the time correlations serve as a critical reference, distinguishing between signal and noise, which in turn enable clear visualization of biological samples. Quantum imaging also addresses the challenge involved in imaging delicate biological structures with minimal photon exposure and sample damage. Here we explore the recent progress in quantum correlation-based imaging, notably its impact on secure imaging and remote sensing protocols as well as on biological imaging. We also exploit the quantum characteristics of heralded single-photon sources (HSPS) combined with decoy-state methods for secure imaging. This method uses Quantum Key Distribution (QKD) principles to reduce measurement uncertainties and protect data integrity. It is highly effective in low-photon-number regimes for producing high-quality, noise-reduced images. The versatility of decoy-state methods with WCSs (WCS) is also discussed, highlighting their suitability for scenarios requiring higher photon numbers. We emphasize the dual advantages of these techniques: improving image quality through noise reduction and enhancing data security with quantum encryption, suggesting significant potential for quantum imaging in various applications, from delicate biological imaging to secure quantum communication.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' un- certainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

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.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the denition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

We study the performance of a classical and quantum magnetic Otto cycle with a quantum dot as a working substance using the Fock-Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, we found in the classical approach an oscillating behavior in the total work that is not perceptible under the quantum formulation. Also, we compare the work and efficiency of this system for different regions of the Entropy, $S(T,B)$, diagram where we found that the quantum version of this engine always shows a reduced performance in comparison to his classical counterpart.

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

Having access to a unique quantum circuit that one wants to protect against use by others is a very likely scenario. However currently users rely on classical computer security schemes, which have known shortcomings. In this chapter we introduce a novel protection scheme along with a survey of other known methods to protect quantum information. In particular we review physically unclonable functions (PUFs), obfuscation, and introduce quantum logic locking.

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured at the same time. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

For the first time in scientific and engineering practice, it is logically and mathematically substantiated, computationally verified and metrologically confirmed that classic and quantum physics, analytical and quantum chemistry, as well as continuous symbolic and discrete digital mathematical analysis, all have computational limits of information entropy, upper 1/10^16 and lower 1/10^64. Mutual displacement of these limits relatively center of Euclidean three-dimensional and of Cartesian two-dimensional space generate sets of quantum dots of mesh topology and weighted average harmonic units of quantum metrics of internal atomic and outer cosmic space, as well as determines limits of communication speed, clock frequency, calculation power and accuracy for any computing machine with subatomic elements of memory. The matrices of functional density and entropy of energy and information fields reconciles classic and quantum physics with continuous and discrete mathematics of special and general relativity.

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

The phenomenal mathematical efficiency of quantum field theories in modern high-speed information and communication systems has a very simple explanation from the point of view of common sense and higher mathematical logic: all of them – quantum cosmology, quantum physics, quantum metrics and quantum calculus – are the self-informational mathematical systems based on symbolic and numerical functional analysis and elementary recursive calculations of interrelated space and time parameters of matter motion in various states of the material environment.For the first time in scientific and engineering practice, it was clearly shown that the information entropy of both standard symbolic and non-standard numerical functional analysis has absolute exact limits of computational accuracy – 1/10^16 and 1/10^64, respectively. Moreover, the second limit determines the maximum level of accuracy of practical quantum metrics and calculations and fully coordinates four branches of classical physics – thermodynamics, electrodynamics, gravidynamics, chromodynamics with special and general relativity.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data (Ingber, 2018). Adaptive Simulated Annealing (ASA) was used for all fits to data. A numerical path-integral for quantum systems, qPATHINT, was used. Objective: The quantum path-integral for Calcium ions was used to derive a closed-form analytic solution at arbitrary time. The quantum effects is parameterized here, whereas the previous 2018 paper applied a nominal ratio of 1/2 to these effects. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used. The quantum path-integral is used to derive a closed-form analytic solution at arbitrary time, and is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that three cases with Subjects (blind to this author) after 1,000,000 visits to the cost function gave: Subject-07 = 0.04, Subject-08 = 0.55, and Subject-09 = 1.00. All other 9 Subjects gave 0.

How does the world around us work and what is real? This question has preoccupied humanity since its beginnings. From the 16th century onwards, it has been periodically necessary to revise the prevailing worldview. But things became very strange at the beginning of the 20th century with the advent of relativity theory and quantum physics. The current focus is on the role of information, there being a debate about whether this is ontological or epistemological. A theory has recently been formulated in which spacetime and gravity emerges from microscopic quantum information, more specifically from quantum entanglement via entanglement entropy. A latest theory describes the emergence of reality itself through first-person perspective experiences and algorithmic information theory. In quantum physics, perception and observation play a central role. Perception, interaction with the environment, requires an exchange of information. Via biochemical projection, information is given an interpretation that is necessary to make life and consciousness possible. The world around us is not at all what it seems.

A simplified version of the quantum teleportation protocol is presented in here. Its experimental confirmation will have deep implications for a better understanding of Quantum Entanglement with a particular projection on Quantum Communications.

It is shown that the representation theory of some finitely presented groups thanks to their $SL_2(\mathbb{C})$ character variety is related to algebraic surfaces. We make use of the Enriques-Kodaira classification of algebraic surfaces and the related topological tools to make such surfaces explicit. We study the connection of $SL_2(\mathbb{C})$ character varieties to topological quantum computing (TQC) as an alternative to the concept of anyons. The Hopf link $H$, whose character variety is a Del Pezzo surface $f_H$ (the trace of the commutator), is the kernel of our view of TQC. Qutrit and two-qubit magic state computing, derived from the trefoil knot in our previous work, may be seen as TQC from the Hopf link. The character variety of some two-generator Bianchi groups as well as that of the fundamental group for the singular fibers $\tilde{E}_6$ and $\tilde{D}_4$ contain $f_H$. A surface birationally equivalent to a $K_3$ surface is another compound of their character varieties.

We propose a quantum version of the well known minimum distance classification model called "Nearest Mean Classifier" (NMC). In this regard, we presented our first results in two previous works. In [34] a quantum counterpart of the NMC for two-dimensional problems was introduced, named "Quantum Nearest Mean Classifier" (QNMC), together with a possible generalization to arbitrary dimensions. In [33] we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding of n-dimensional patterns into density operators is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted to: i) compare the NMC and QNMC performance on different datasets; ii) study the effects of the non-invariance under uniform rescaling for the QNMC.

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the author. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The author's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

We develop a renormalizable model of Quantum General Relativity (QGR). We do this by building on earlier work with quantum electrodynamics (QED). Working with the Feynman path integral (FPI) approach to QED, we generalize the paths from varying in space to varying in space and time. This gives the standard results plus dispersion in time of order attoseconds or left. Over longer times, the dispersion in time averages out, but at attosecond times it should be detectable with current technology. As an unexpected but welcome side-effect, the approach caused the usual loop integrals to be finite. Since the usual UV divergences are significantly harder to renormalize in QGR than in QED, and since using paths in time plus space is definitely more in keeping with the general spirit of GR, we here apply the same approach to QGR. We show that with an appropriate choice of gauge (trace-reversed de Donder gauge) we can extend the earlier results to include QGR. Sub-attosecond measurements of individual gravitons are not within our reach, but at least the ultraviolet divergences in QGR are contained in the same way. We have therefore a renormalizable model of QGR

Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or in transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing imposes a major threat on the modern cryptosystems based on modular arithmetic whereby, even the computationally hard problems which constitute for the strength of the modular arithmetic ciphers could be solved in deterministic time. This threat triggered post-quantum cryptography research in order to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides a review of the various post-quantum cryptography and, in specific, code-based cryptography research dimensions. The research directions that are yet to be explored in code-based cryptography research is another key contribution of this paper.

Chemistry has been viewed as one of the most fruitful near-term applications to science of quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Much less effort has been placed on how one finishes these calculations by using the results from the quantum computer (on the active region of the molecule) and embeds them back into the remainder of the molecule in order to determine the properties of the entire molecule. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with classical algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, applications are made to a model of financial options, Statistical Mechanics of Financial Markets (SMFM). These applications were published in many papers since the 1980's. This project only uses Classical (super-)computers to include quantum features of these models. Since 1989, an optimization code, Adaptive Simulated Annealing (ASA), has been to fit parameters in such models. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space by SMFM applies nonlinear nonequilibrium multivariate statistical mechanics to fit parameters in conditional short-time probability distributions, while the quantum space described by qPATHINT deals specifically with quantum systems, e.g., quantum money. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

In this note, we demonstrate the quantum no-hiding theorem of Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)] using the IBM 5Q quantum processor. We also analyze the circuit using the ZX calculus of Coecke and Duncan [New J Phys. 13(4), 043016 (2011)], which provides a pictorial/category-theoretic demonstration of the no-hiding theorem.

In this paper we try to demonstrate that the classical model of certainty factos for dealing with innacurate knowledge can be efficiently implemented in a quantum environment. For this, we assume that certainty factors are strongly correlated with the quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. We then build a use case: an inferential network to be implemented in both, the classical approach and the corresponding quantum circuit. Both implementations have been used to compare the behavior of the classical and the quantum approaches when confronted with the same hypothetical case. We analyze three different situations: (1) Only Imprecision (which refers to inaccuracy in declarative knowledge or facts) is present in the use case, (2) Only Uncertainty (which refers to inaccuracy in procedural knowledge or rules) is present in the use case, and (3) Both Imprecision and Uncertainty are present in the use case. Finally, we analyze the results to reach a conclusion about the eventually intrinsic probabilistic nature of the certainty factors model and to pave the way for future quantum implementations of this method for handling inaccurate knowledge.

Classical physics meets the obstacle of describing a point particle because from everyday experience we know that objects occupy a certain volume. We overcome this obstacle by using the equivalence principle for electric energy and describe a curved spacetime of fluid nature. From thereon by using the notion of a point volume the rest of the thermodynamic quantities appear.

We present detailed models at the hydrodynamics and decoherence phenomena observed in ideal quantum gases. The model is expressed in terms of a quantum field theory, where the action involves both hydrodynamic and decoherence terms. The density-current relation is derived, and the current Green function is introduced. The effective action for two fields is presented, and the physical field is defined in terms of the bare action. Identities such as CTP symmetry, transposition, and the Ward identity are discussed. The Green function and its inverse for different components are also explored. These notes provide a comprehensive understanding of the theoretical framework for studying the hydrodynamics and decoherence of ideal quantum gases.

Black hole collision produce gravitational radiation which is generally thought in a quantum limit to be gravitons. The stretched horizon of a black hole contains quantum information, or a form of quantum hair, which in a coalescence of black holes participates in the generation of gravitons. This may be facilitated with a Bohr-like approach to black hole (BH) quantum physics with quasi-normal mode (QNM) approach to BH quantum mechanics. Quantum gravity and quantum hair on event horizons is excited to higher energy in BH coalescence. The near horizon condition for two BHs right before collision is a deformed AdS spacetime. These excited states of BH quantum hair then relax with the production of gravitons. This is then argued to define RT entropy given by quantum hair on the horizons. These qubits of information from a BH coalescence should then appear in gravitational wave (GW) data. This is a form of the standard AdS/CF T correspondence and the Ryu-Takayanagi (RT) formula [1]. The foundations of physics is proposed to be quantum information and a duality between spacetime observables and quantum fields.

The ability to control the flow of quantum information deterministically is useful for scaling up quantum computation. In this paper, we demonstrate a controllable quantum switchboard which directs the teleportation protocol to one of two targets, fully dependent on the sender’s choice. The quantum switchboard additionally acts as a optimal quantum cloning machine. We also provide a physical implementation of the proposal using a coupled-cavity array. The proposed switchboard can be utilized for the efficient routing of quantum information in a large quantum network.

Phase transitions- both in the classical and in the quantum version- are the perfect playground for appreciating universality at work. Indeed, the fine details become unimportant and a classification in very few universality classes is possible. Very recently, a striking deviation from this picture has been discovered: some antiferromagnetic spin chains with competing interactions show a different set of phase transitions depending on the parity of number of spins in the chain. The aim of this article is to demonstrate that the same behavior also characterizes the most simple quantum spin chain: the Ising model in a transverse field. By means of an exact solution based on a Wigner-Jordan transformation, we show that a first order quantum phase transition appears at zero applied field in the odd spin case, while it is not present in the even case. A hint of a possible physical interpretation is given by the combination of two fact: at the point of the phase transition, the degeneracy of the ground state in the even and the odd case substantially differ, being respectively 2 and 2N, with N the number of spins; the spin of the most favorable kink states changes at that point.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.

Scattering of a probe laser pulse by an intense light spring in QED vacuum is considered. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with scattering of light by a rotating black hole, usually called Penrose superradiance. Here the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components with slightly different frequencies, the energy profile of the intense laser beam rotates with a frequency that depends on the frequency difference. The nonlinear properties of quantum vacuum are described by first order Euler-Heisenberg Lagrangian. It is shown that, in such a configuration, nonlinear photon-photon coupling leads to scattered radiation, with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favourable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium.

The rapid development of quantum computing devices promises powerful machines with capabilities that solve a wide range of problems that traditional computers cannot. Therefore, quantum computers generate new threats at unprecedented speed and scale and specifically pose an enormous threat to encryption. Lattice-based cryptography is considered to be the rival to a quantum computer attack and the future of post-quantum cryptography. So, cryptographic protocols based on lattices have a variety of benefits, like security, efficiency, lower energy consumption, and speed. In this work, we study the most well-known lattice-based cryptosystems while a systematic evaluation and comparison is presented also, and focuses on their strengths and weaknesses.

Image synthesis poses a challenging problem that researchers in computer vision and machine learning have been grappling with for several decades. Numerous machine learning techniques have emerged and proven effective in generating high-fidelity artificial images. This study breaks new ground by exploring image synthesis through generative learning using the D-Wave 2000Q quantum annealer, marking the first attempt to address the issue of generative image synthesis on a Quantum Processing Unit (QPU). Alongside executing image synthesis on the quantum annealer, this research also compares its performance with existing classical models and delves into resolving the Generative Learning Trilemma.

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.

Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue that quantum chaos came as an indispensable rectification, removing inconsistencies related to entropy in classical chaos: Bottom-up information currents require an inexhaustible entropy production and a diverging information density in phase space, reminiscent of Gibbs' paradox in Statistical Mechanics. It is shown how a mere discretization of the state space of classical models already entails phenomena similar to hallmarks of quantum chaos, and how the unitary time evolution in a closed system directly implies the “quantum death” of classical chaos. As complementary evidence, I discuss quantum chaos under continuous measurement. Here, the two-way exchange of information with a macroscopic apparatus opens an inexhaustible source of entropy and lifts the limitations implied by unitary quantum dynamics in closed systems. The infiltration of fresh entropy restores permanent chaotic dynamics in observed quantum systems. Could other instances of stochasticity in quantum mechanics be interpreted in a similar guise? Where observed quantum systems generate randomness, that is, produce entropy without discernible source, could it have infiltrated from the macroscopic meter? This speculation is worked out for the case of spin measurement.

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

The experiment proposed by Bose et al aims to show the non classicality of gravity through entanglement. This paper seeks to establish optimal conditions under which the entanglement would be maximized. The assumptions made by Bose et al to come to the conclusion of quantized gravity would also be discussed along with alternate conclusions that could arise from the experiment.

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.

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.

Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.

This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary "particles''. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. In this paper, generation, characterisation and application of a genuine genuinely entangled seven-qubit resource state is studied. Theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation as well as three schemes for undertaking tripartite quantum state sharing are presented.

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in a recent study by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

We study the changes in quantum Fisher information (QFI) values for one quantum system consisting of a superposition of W and GHZ states. In a recent work [6], QFI values of this mentioned system studied. In this work, we extend this problem for the changes of QFI values in some noisy channels. We show the change in QFI depending on noise parameters. We report interesting results for different type of decoherence channels.

In this article we presented an application of the quantum cosmological model in teleparallel gravity. Working with a vacuum solution, the gravitational energy density is quantized with the Weyl procedure and we obtain a discrete expression for the gravitational energy. As an immediate consequence the empty space exhibits an expansion for an early universe.