Quantum separability criteria from bipartite systems to multipartite systems based on generalized Bloch representation

TL;DR

This paper introduces a new framework using generalized Bloch representation and matrix unfolding to improve the detection of bipartite and multipartite quantum entanglement.

Contribution

It develops a novel parameterized correlation tensor and extends it to multipartite systems, enhancing entanglement detection capabilities.

Findings

Improved entanglement detection performance demonstrated through examples.

New separability criteria applicable to both bipartite and multipartite systems.

Enhanced detection capability over existing methods.

Abstract

Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting bipartite and multipartite entanglements. We construct a novel parameterized extended correlation tensor via the generalized Bloch representation under an arbitrary orthogonal basis, which improves the performance of entanglement detection. Moreover, we employ the generalized matrix unfolding to generalize the extended correlation tensor construction to multipartite systems, obtaining separability criteria for multipartite entanglement. Detailed examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement.