### 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 language | English (US) |
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Pages (from-to) | 753-774 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 281 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 2008 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*281*(3), 753-774. https://doi.org/10.1007/s00220-008-0493-6