Separable states and positive maps II

TL;DR

This paper explores new characterizations of separable states in quantum systems using duality between linear functionals and maps, focusing on abelianness and tensor products of specific C*-algebras.

Contribution

It introduces two novel criteria for separability based on the structure of linear maps and algebraic properties, extending previous theoretical frameworks.

Findings

Separable states characterized by abelianness of the definite set.

New criteria involving tensor products of nuclear and UHF C*-algebras.

Enhanced understanding of the duality between linear functionals and maps.

Abstract

Using the natural duality between linear functionals on tensor products of C*-algebras with the trace class operators on a Hilbert space H and linear maps of the C*-algebra into B(H), we give two characterizations of separability, one relating it to abelianness of the definite set of the map, and one on tensor products of nuclear and UHF C*-algebras