TY - JOUR

T1 - Entanglement of positive definite functions on compact groups

AU - Korbicz, J. K.

AU - Wehr, J.

AU - Lewenstein, M.

PY - 2008/8

Y1 - 2008/8

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-008-0493-6

DO - 10.1007/s00220-008-0493-6

M3 - Article

AN - SCOPUS:45849108740

VL - 281

SP - 753

EP - 774

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -