Entanglement of positive definite functions on compact groups

J. K. Korbicz, Jan Wehr, M. Lewenstein

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of the Horodecki Theorem, giving a necessary and sufficient criterion for separability of such functions. The resulting characterisation is given in terms of mappings of the space of continuous functions, preserving positive definiteness. A relation between the developed group-theoretical formalism and the conventional one, given in terms of density matrices, is established through the non-commutative Fourier analysis. It shows that the presented method plays the role of a "generating function" formalism for the theory of entanglement.

Original languageEnglish (US)
Pages (from-to)753-774
Number of pages22
JournalCommunications in Mathematical Physics
Volume281
Issue number3
DOIs
Publication statusPublished - Aug 2008

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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