A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-toquantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.

This work presents a satellite alternative to quantum repeaters based on the terrestrial laid of optical fiber, where the latter have the following disadvantages: a propagation speed (v) equal to 2/3 of the speed of light (c), losses and an attenuation in the material that requires the installation of a repeater every 50 km, while satellite repeaters can cover greater distances at a speed v = c, with less attenuation and losses than in the case of optical fiber except for relative environmental aspects to the ground-sky link, that is, clouds that can disrupt the distribution of entangled photons. Two configurations are presented, the first one of a satellite and the second one of two satellites in the event that both points on the ground cannot access the same satellite. Finally, a series of implementations for evaluating the performance and robustness of both configurations are implemented on a 5 qubits IBM Q processor.

We demonstrate that quantum information processing (QIP) completely rests on quantum Fourier transform (QFT), and 190 years after his death, the work of Jean-Baptiste Joseph Fourier is more present than ever in one of the most important pillars of physics: QIP. Specifically, this study shows the impact of QFT on the main tool of quantum communication: entanglement, with a particular emphasis on its spectral nature, whose study is completed when entanglement is used in teleportation, and quantum secret sharing. Finally, a better understanding of the spectral nature of quantum entanglement will lead to better protocols for quantum communications, in general, and quantum cryptography, in particular.

This study establishes, for the first time in literature, that quantum entanglement, as well as the most important protocol derived from it, that is, quantum teleportation, completely rest on the Quantum Fourier Transform. This highlights the spectral nature of both protocols with important consequences on quantum computing, quantum communications, and quantum cryptography, with a particular emphasis on quantum Internet. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

This study demonstrates entanglement can be exclusively constituted by quantum Fourier transform (QFT) blocks. A bridge between entanglement and QFT will allow incorporating a spectral analysis to the already traditional temporal approach of entanglement, which will result in the development of new more performant, and fault-tolerant protocols to be used in quantum computing as well as quantum communication, with particular emphasis in the future quantum Internet.