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IEEE International Conference on Acoustics Speech and Signal Processing

Blind qubit state disentanglement with Quantum processing: Principle, criterion and algorithm using measurements along two directions

Yannick Deville, Alain Deville

Published May 1, 2014• 14 citations
Publisher

Abstract

In the framework of Blind Quantum Source Separation, we investigate the adaptation of a separating system which receives coupled quantum bit (qubit) states and processes them with quantum means in its feedforward path, to uncouple them. We propose the first separation principle which ensures that the output qubit states of this system are disentangled and that they restore the non-entangled source qubit states up to limited indeterminacies. This separation principle exploits measurements of output spin components along two directions and has some links with the non-quantum Independent Component Analysis (ICA) principle. It opens the way to various practical separation criteria and algorithms, some of which are described here.

DOI
10.1109/icassp.2014.6854800

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In the framework of Blind Quantum Source Separation, we investigate the adaptation of a separating system which receives coupled quantum bit (qubit) states and processes them with quantum means in its feedforward path, to uncouple them. We propose the first separation principle which ensures that the output qubit states of this system are disentangled and that they restore the non-entangled source qubit states up to limited indeterminacies. This separation principle exploits measurements of output spin components along two directions and has some links with the non-quantum Independent Component Analysis (ICA) principle. It opens the way to various practical separation criteria and algorithms, some of which are described here.
This paper deals with Blind Quantum Source Separation (BQSS). The proposed separating system only receives observed quantum states, each obtained after two quantum bits (qubits) were first independently initialized with values that this system does not know and then coupled according to a quantum operator involving parameter values that the separating system does not know a priori. This system aims at restoring the information contained in the initial qubit states. We previously tackled this problem by first converting the observed quantum state into data which have a classical (i.e. non-quantum) form and then only processing the latter data with classical means. We here propose a new approach, based on a separating system which uses quantum processing means (consisting of a specific unitary operator) in its feedforward path. Classical processing is only used in the feedback path of this system, to adapt its transfer function. The proposed adaptation method is based on binary-valued monodirectional output measurements and related to quantum disentanglement. We also analyze its relationships with classical Independent Component Analysis. We prove that this BQSS method partly restores the initial two-qubit states: it determines their components up to some phase and permutation indeterminacies.
Our recent investigations of blind quantum source separation and process tomography methods for Heisenberg-coupled quantum bits (qubits) were focused on introducing a new separation principle, based on output disentanglement. We here extend them by proposing a more advanced implementation of their cost function and optimization algorithm. This leads us to move from a feedback to a feedforward adapting block, which avoids potential issues related to feedback in quantum circuits. The number of quantum source state preparations required to blindly adapt the separating system is thus strongly decreased (roughly from 107to 104), yielding much faster adaptation.
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.
System identification and inversion are two closely related problems, which lead to various configurations. In the quantum framework, system identification was only studied in the non-blind (or supervised) mode, i.e. with known input states (in addition to known output states). It is then called quantum process tomography. We here develop its blind (or unsupervised) version, operating with unknown (unentangled) input states (which are here not controlled by an automated loop). Our approach takes advantage of the blind quantum source separation (i.e. blind multi-qubit system inversion) methods based on disentanglement that we recently introduced. It is detailed for Heisenberg spin coupling and could be extended to other classes of processes. It estimates the parameter values of the Heisenberg Hamiltonian.
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.