Criteria of genuine multipartite entanglement based on correlation tensors

TL;DR

This paper introduces a simplified method for detecting genuine multipartite entanglement using correlation tensors, involving Schmidt decomposition and local unitary transformations, applicable to higher-dimensional systems.

Contribution

It proposes a new criterion based on the trace norm of correlation tensors, improving detection of genuine multipartite entanglement over existing methods.

Findings

Detects more genuinely entangled states

Applicable to higher-dimensional tripartite systems

Uses correlation tensor trace norm as a key measure

Abstract

We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems.