Blind separation of quantum states: estimating two qubits from an isotropic Heisenberg spin coupling model

Authors:
Yannick Deville;Alain Deville
Affiliations:
Université Paul Sabatier Toulouse 3, CNRS, Laboratoire d'Astrophysique de Toulouse-Tarbes, UMR, Toulouse, France;Université de Provence, Bâtiment IRPHE, Marseille Cedex 13, France
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

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Abstract

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. 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 Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce new nonlinear mixture models for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of these models. We propose practical data processing methods for performing inversions.