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International symposium on image and signal processing and analysis/ISPA ...

A blind quantum source separation method based on mutual information for retrieving two qubits with cylindrical-symmetry heisenberg coupling

Devillé

Published Jan 1, 2011• 0 citations
OpenAlex

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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.

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Effect of indirect dependencies on "Maximum likelihood blind separation of two quantum states (qubits) with cylindrical-symmetry Heisenberg spin coupling"

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In a previous paper [1], we investigated the Blind Source Separation (BSS) problem, for the nonlinear mixing model that we introduced in that paper. We proposed to solve this problem by using a maximum likelihood (ML) approach. When applying the ML approach to BSS problems, one usually determines the analytical expressions of the derivatives of the log-likelihood with respect to the parameters of the considered mixing model. In the literature, these calculations were mainly considered for linear mixtures up to now. They are more complex for nonlinear mixtures, due to dependencies between the considered quantities. Moreover, the notations commonly employed by the BSS community in such calculations may become misleading when using them for nonlinear mixtures, due to the above-mentioned dependencies. In this document, we therefore explain this phenomenon, by showing the effect of indirect dependencies on the application of the ML approach to the mixing model considered in [1]. This yields the explicit expression of the complete derivative of the log-likelihood associated to that mixing model.

arXiv:0906.0062•May 30, 2009•1 citation
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.
In a previous paper [1], we investigated the Blind Source Separation (BSS) problem, for the nonlinear mixing model that we introduced in that paper. We proposed to solve this problem by using a maximum likelihood (ML) approach. When applying the ML approach to BSS problems, one usually determines the analytical expressions of the derivatives of the log-likelihood with respect to the parameters of the considered mixing model. In the literature, these calculations were mainly considered for linear mixtures up to now. They are more complex for nonlinear mixtures, due to dependencies between the considered quantities. Moreover, the notations commonly employed by the BSS community in such calculations may become misleading when using them for nonlinear mixtures, due to the above-mentioned dependencies. In this document, we therefore explain this phenomenon, by showing the effect of indirect dependencies on the application of the ML approach to the mixing model considered in [1]. This yields the explicit expression of the complete derivative of the log-likelihood associated to that mixing model.