Detecting multipartite entanglement via complete orthogonal basis

TL;DR

This paper introduces a new method using complete orthogonal basis (COB) to detect genuine tripartite and multipartite entanglement more effectively than previous criteria, simplifying computations in quantum systems.

Contribution

The paper develops operational criteria based on COB for detecting multipartite entanglement, improving detection capabilities over existing methods.

Findings

Criteria detect more entangled states than previous methods

Simplifies computations using COB in quantum state analysis

Effective in arbitrary dimensional multipartite systems

Abstract

We study genuine tripartite entanglement and multipartite entanglement in arbitrary $n$-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of generators, the density matrix with COB operators has one uniformed type of generators which may simplify related computations. We take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement. We first convert the general states to simpler forms by using the relationship between general symmetric informationally complete measurements and COB. Then we derive an operational criteria to detect genuine tripartite entanglement. We study multipartite entanglement in arbitrary dimensional multipartite systems. By providing detailed examples, we demonstrate that our criteria can detect more genuine entangled and multipartite entangled states than the previously existing criteria.