During the last 25 years the scientific community has coexisted with the most fascinating protocol due to Quantum Physics: quantum teleportation (QTele), which would have been impossible if quantum entanglement, so questioned by Einstein, did not exist. In this work, a complete architecture for the teleportation of Computational Basis States (CBS) is presented. Such CBS will represent each of the possible 24 classical bits commonly used to encode every pixel of a 3-color-channel-image (red-green-blue, or cyan-yellow-magenta). For this purpose, a couple of interfaces: classical-to-quantum (Cl2Qu) and quantum-to-classical (Qu2Cl) are presented with two versions of the teleportation protocol: standard and simplified.

During the last century, entanglement was the bone of contention between the two main pillars of Physics: General Relativity (GR) and Quantum Mechanics (QM). This began in 1935 with the Einstein-Podolsky-Rosen paradox (EPR paradox) which concluded that although Quantum Mechanics is not wrong, it is an incomplete theory to represent physical reality. In this paper it is demonstrated that some byproducts resulting from entanglement and which we will call avatars act as a hinge that link both theories making the completeness of QM clear. Moreover, a thorough analysis of the non-locality of this effect will be carried out. Besides, it is demonstrated that entanglement is an instantaneous phenomenon and that it does not require the use of a superluminal signaling for this purpose. Finally, the avatars will also appear in each wormhole resulting from an entanglement process (WREP) demonstrating that they are traversable with an equivalent path of null length which can be crossed in a null time with all that this implies in Quantum Communications.

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.

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum - not taken into account by Fourier theory and let alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N2) for images, c) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.