Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Separability of Mixed States: Necessary and Sufficient Conditions

Michal Horodecki, Pawel Horodecki, Ryszard Horodecki

Abstract

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.

Separability of Mixed States: Necessary and Sufficient Conditions

Abstract

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for and systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.

Paper Structure

This paper contains 4 theorems, 27 equations.

Key Result

Lemma 1

For any inseparable state $\tilde{\varrho}\in {\cal A}_1\otimes{\cal A}_2$ there exists Hermitian operator $\tilde{A}$ such that for any separable $\sigma$.

Theorems & Definitions (4)

  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Theorem 3