Separable states and positive maps

TL;DR

This paper explores the relationship between separability, entanglement, and positivity conditions of states and linear maps in quantum information theory, using duality between functionals and maps.

Contribution

It introduces a duality framework connecting states and linear maps to analyze separability and entanglement properties.

Findings

Characterizes separability and entanglement via duality

Analyzes the Peres condition in the context of positive maps

Provides insights into positivity properties of linear 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 study the relationship between separability, entanglement and the Peres condition of states and positivity properties of the linear maps.