Separability criterion for bipartite states and its generalization to multipartite systems

TL;DR

This paper introduces symmetric operators as entanglement witnesses, generalizing Wootters' separability criterion from two-qubit states to bipartite and multipartite quantum systems of arbitrary dimensions.

Contribution

The paper presents a new class of symmetric operators that serve as entanglement witnesses, enabling a generalized separability criterion for complex quantum systems.

Findings

Symmetric operators can be represented by matrices with two nonzero elements.

These operators generalize Wootters' criterion to higher-dimensional systems.

The approach applies to both bipartite and multipartite quantum states.

Abstract

A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their arbitrary linear combinations are found to be entanglement witnesses. By using these symmetric operators, Wootters' separability criterion for two-qubit states can be generalized to bipartite and multipartite systems in arbitrary dimensions.