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Entanglement and Hilbert space geometry for systems with a few qubits

Published online by Cambridge University Press:  01 December 2007

REMY MOSSERI  and
PEDRO RIBEIRO
REMY MOSSERI
Affiliation:
Laboratoire de Physique Théorique de la Matire Condense, CNRS UMR 7600, Université Pierre et Marie Curie Paris 6, Tour 24, Boite 121, 4 place Jussieu, 75252 Paris Cedex 05France Email: mosseri@ccr.jussieu.frpedro@lptmc.jussieu.fr
PEDRO RIBEIRO
Affiliation:
Laboratoire de Physique Théorique de la Matire Condense, CNRS UMR 7600, Université Pierre et Marie Curie Paris 6, Tour 24, Boite 121, 4 place Jussieu, 75252 Paris Cedex 05France Email: mosseri@ccr.jussieu.frpedro@lptmc.jussieu.fr
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Abstract

This paper reviews recent attempts to describe the two- and three-qubit Hilbert space geometries. In the first part, this is done with the help of Hopf fibrations of hyperspheres. It is shown that the associated Hopf map is strongly sensitive to states’ entanglement content. In the two-qubit case, a generalisation of the celebrated one-qubit Bloch sphere representation is described. In the second part, we present Hilbert space discrete versions, which are comparable to polyhedral approximations of spheres in standard geometry.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 6 , December 2007 , pp. 1117 - 1132
Copyright
Copyright © Cambridge University Press 2007

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