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ICA Separability of Nonlinear Models with References: General Properties and Application to Heisenberg-Coupled Quantum States (Qubits)

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Latent Variable Analysis and Signal Separation (LVA/ICA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6365))

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.

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References

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Author information

Authors and Affiliations

  1. Laboratoire d’Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, 14 Av. Edouard Belin, 31400, Toulouse, France

    Yannick Deville

Authors
  1. Yannick Deville
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Editor information

Editors and Affiliations

  1. Dept. of Electrical Engineering, Universitè d’Evry Val d’Essone, 40 rue du Pelvoux, 91020, Courcouronnes, France

    Vincent Vigneron

  2. Laboratoire I3S, Les Algorithmes - Euclide-B, BP 121, Université de Nice-Sophia Antipolis, 2000 Route des Lucioles, 06903, Sophia Antipolis Cedex, France

    Vicente Zarzoso

  3. School of Engineering, Dept. of Telecommunications, ISITSchool of Engineering, Dept. of Telecommunications, ISITV, Université de Toulon, Avenue George Pompidou, BP 56, La Valette du Var, Cedex, 83162, France

    Eric Moreau

  4. INRIA France, Equipe-projet METISS, Centre de Recherche INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042, Rennes cedex, France

    Rémi Gribonval

  5. INRIA France, Equipe-projet METISS, Centre de Recherche INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042, Rennes Cedex, France

    Emmanuel Vincent

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© 2010 Springer-Verlag Berlin Heidelberg

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Deville, Y. (2010). ICA Separability of Nonlinear Models with References: General Properties and Application to Heisenberg-Coupled Quantum States (Qubits). In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15995-4_22

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  • DOI: https://doi.org/10.1007/978-3-642-15995-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15994-7

  • Online ISBN: 978-3-642-15995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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