On the tensor convolution and the quantum separability problem

TL;DR

This paper explores the connection between tensor convolution on locally compact abelian groups and the quantum separability problem, providing a new mathematical formulation for deciding entanglement.

Contribution

It introduces a novel approach linking tensor convolution with quantum separability, expanding the mathematical tools available for entanglement detection.

Findings

Tensor convolution relates to the quantum separability problem.

Provides an equivalent formulation for deciding separability.

Extends the mathematical framework for entanglement analysis.

Abstract

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary locally compact abelian group, give rise to formulation of an equivalent problem to the separability one.