Separability from Multipartite Measures

TL;DR

This paper introduces the third-order negativity as a comprehensive criterion for determining full separability in tripartite pure states and extends this approach to mixed states and multipartite qudit systems.

Contribution

It establishes the third-order negativity as a necessary and sufficient separability measure and generalizes the criteria to higher-dimensional systems and applications in conformal field theory.

Findings

Third-order negativity fully characterizes separability of tripartite pure states.

Complete state characterization involves multiple bipartite, tripartite, and quadripartite measures.

The approach extends to multipartite qudit systems and has applications in conformal field theory.

Abstract

We show that the third-order negativity provides a necessary and sufficient criterion for full separability of tripartite pure states, and extend this to mixed states beyond bipartite diagnostics such as negativity. As a minimal nontrivial example, a four-qubit pure state has three-qubit mixed reductions; its complete characterization requires six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. We further generalize these separability criteria to multipartite qudit systems and discuss an application to conformal field theory.