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Concepts and Criteria for Blind Quantum Source Separation and Blind Quantum Process Tomography

1
Institut Matériaux Microélectronique et Nanosciences de Provence (IM2NP), Aix-Marseille Université, 13397 Marseille, France
2
Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, 31400 Toulouse, France
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(7), 311; https://doi.org/10.3390/e19070311
Received: 6 April 2017 / Revised: 9 June 2017 / Accepted: 23 June 2017 / Published: 6 July 2017
(This article belongs to the Special Issue Quantum Information and Foundations)
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Abstract

Blind Source Separation (BSS) is an active domain of Classical Information Processing, with well-identified methods and applications. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS), with a recent extension towards Blind Quantum Process Tomography (BQPT). This article investigates the use of several fundamental quantum concepts in the BQSS context and establishes properties already used without justification in that context. It mainly considers a pair of electron spins initially separately prepared in a pure state and then submitted to an undesired exchange coupling between these spins. Some consequences of the existence of the entanglement phenomenon, and of the probabilistic aspect of quantum measurements, upon BQSS solutions, are discussed. An unentanglement criterion is established for the state of an arbitrary qubit pair, expressed first with probability amplitudes and secondly with probabilities. The interest of using the concept of a random quantum state in the BQSS context is presented. It is stressed that the concept of statistical independence of the sources, widely used in classical BSS, should be used with care in BQSS, and possibly replaced by some disentanglement principle. It is shown that the coefficients of the development of any qubit pair pure state over the states of an orthonormal basis can be expressed with the probabilities of results in the measurements of well-chosen spin components. View Full-Text
Keywords: blind source separation (BSS); qubit pair; exchange coupling; entangled pure state; unentanglement criterion; probabilities in quantum measurements; independence of random quantum sources blind source separation (BSS); qubit pair; exchange coupling; entangled pure state; unentanglement criterion; probabilities in quantum measurements; independence of random quantum sources
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Deville, A.; Deville, Y. Concepts and Criteria for Blind Quantum Source Separation and Blind Quantum Process Tomography. Entropy 2017, 19, 311.

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