Separability criteria based on the Weyl operators

TL;DR

This paper introduces a new separability criterion for quantum states using Weyl operators, providing an effective method to detect entanglement and construct teleportation detecting operators.

Contribution

It proposes a novel Bloch decomposition based on Weyl basis, offering an alternative separability characterization and entanglement detection method.

Findings

Effective detection of entanglement in isotropic states

Successful identification of entanglement in Bell-diagonal states

Construction of a teleportation detecting operator

Abstract

Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We shaw that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.