ICA separability of nonlinear models withn references: general properties and application to Heisenberg-coupled quantum states (qubits)

Authors:
Yannick Deville
Affiliations:
Laboratoire d'Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, Toulouse, France
Venue:
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Year:
2010

Citing 2
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Exact and approximate quantum independent component analysis for qubit uncoupling

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Abstract

Relatively few results were reported about the separability of given classes of nonlinear mixtures by means of the ICA criterion. We here prove the separability of a wide class of nonlinear global (i.e. mixing + separating) models involving "reference signals", i.e. unmixed signals. This work therefore concerns a nonlinear extension of linear adaptive noise cancellation (ANC).We then illustrate the usefulness of our general results by applying them to a model of Heisenberg-coupled quantum states. This paper opens the way to practical ICA methods for nonlinear mixtures encountered in various applications.