Entanglement of positive definite functions on compact groups

Details Entanglement of positive definite functions on compact groups Entanglement of positive definite functions on compact groups

2007-05-21

arxiv.org/abs/0705.2965v4

Comm. Math. Phys. 281, 753 (2008)

Physics

Quantum Physics

published version

Scientific paper

10.1007/s00220-008-0493-6

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of 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. The 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.

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