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Asia-Pacific Conference on Communications (APCC)

Analytical performance analysis for blind quantum source separation with time-varying coupling

Yannick Deville, Alain Deville, Simon Rebeyrol, Ali Mansour

Published Dec 1, 2017• 1 citation
Publisher

Abstract

Classical, i.e. non-quantum, blind source separation (BSS) methods estimate unknown source signals by using only mixed signals obtained by transferring these source signals through a mixing transform, which typically has unknown parameter values. We developed quantum versions of BSS, in which the mixing parameter values almost always remained fixed over time. We here show that rapidly varying mixing is much more complex to handle, because unknown quantum states cannot be cloned, i.e. copied. We avoid this issue thanks to a specific separating system based on a master-slave structure. We provide an original analytical analysis of the performance of that structure, depending on the mismatch between its master and slave inverting blocks.

DOI
10.23919/apcc.2017.8303976

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Classical, i.e. non-quantum, blind source separation (BSS) methods estimate unknown source signals by using only mixed signals obtained by transferring these source signals through a mixing transform, which typically has unknown parameter values. We developed quantum versions of BSS, in which the mixing parameter values almost always remained fixed over time. We here show that rapidly varying mixing is much more complex to handle, because unknown quantum states cannot be cloned, i.e. copied. We avoid this issue thanks to a specific separating system based on a master-slave structure. We provide an original analytical analysis of the performance of that structure, depending on the mismatch between its master and slave inverting blocks.
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Many methods for processing classical or quantum data are based on estimating some parameters, e.g. those of adaptive filters, artificial neural networks (including deep learning approaches), blind source separation systems or quantum gates. For classical signals, these methods include stochastic algorithms, such as stochastic gradient descent. We here first introduce a partly related, general, type of stochastic algorithms for quantum data and we prove the asymptotic efficiency of the proposed estimator. We then show the attractiveness of this stochastic approach for the quantum version of blind multiple-input multiple-output system identification and blind source separation: the resulting model estimation methods can operate with a single copy of each considered quantum state, whereas the previous methods require many copies of the same (unknown) states to be available and are thus "less blind". Numerical tests show that good performance is obtained with 104such quantum states.
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Blind source separation (BSS) and quantum information processing (QIP) are two recent and rapidly evolving fields. No connection has ever been made between them to our knowledge, except in our initial paper, However, future practical QIP systems will probably involve "observed mixtures", in the BSS sense, of quantum states (qubits), e.g. associated to coupled spins. We here investigate how individual qubits may be retrieved from cylindrical-symmetry Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce a new nonlinear mixture model for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of this model. We propose practical data processing methods for (i) estimating the mixing parameter with a maximum likelihood approach and (ii) performing inversion to retrieve the sources. This yields a major extension as compared to our previous paper, not only in terms of considered spin coupling model, but also because we here introduce a much more powerful mixture estimation procedure.
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.