Entanglement of positive definite functions on compact groups

TL;DR

This paper introduces a framework for understanding entanglement of positive definite functions on compact groups, extending quantum entanglement concepts to a group-theoretic setting with a new separability criterion.

Contribution

It develops an infinite-dimensional analog of the Horodecki Theorem for positive definite functions, linking group theory and quantum entanglement analysis.

Findings

Established a necessary and sufficient criterion for separability.

Connected group-theoretic formalism with density matrix approach.

Extended entanglement concepts to continuous functions on compact groups.

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 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.