Detection of entanglement for multipartite quantum states

TL;DR

This paper introduces a simplified method using generalized Pauli operators to detect genuine tripartite and multipartite entanglement in quantum states, improving detection capabilities over previous techniques.

Contribution

The authors develop a new, simplified representation-based criterion for detecting multipartite entanglement, applicable to arbitrary dimensions, and demonstrate its effectiveness through examples.

Findings

The method detects more entangled states than previous approaches.

It provides operational criteria for genuine tripartite entanglement.

The approach simplifies computation using generalized Pauli operators.

Abstract

We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states by using the representations with generalized Pauli operators of a density matrices. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra $\mathfrak{su}(d)$, the representation with generalized Pauli operators has one uniformed type of generators and it simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more entangled states than previous methods as backed by detailed examples.