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Signals and communication technology

Quantum-Source Independent Component Analysis and Related Statistical Blind Qubit Uncoupling Methods

Yannick Deville, Alain Deville

Published Jan 1, 2014• 14 citations
Publisher
DOI
10.1007/978-3-642-55016-4_1

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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.
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.
System identification, system inversion and its multiple-signal extension to source separation, including non-blind and blind (i.e. unsupervised) configurations, are major topics in classical, i.e. nonquantum, signal processing. Their application fields especially include communications, where they are often referred to as (possibly blind and MIMO) channel identification / estimation and channel equalization. Some of their configurations have also been extended to quantum channels. In this paper, we focus on such channels and on the most challenging configurations, namely blind and multiplequbit ones, hence with main emphasis on source separation. In this framework, two classes of methods were previously proposed for two-qubit configurations and a specific type of channels. We here first define their extensions to any number of qubits and general channels. For that configuration too, we then propose a third class of methods and we analyze its relationships with the previous two. This leads us to provide new general insight into the connections between the unentanglement of a pure quantum state and the statistical independence of associated measurement components.