Separability from Multipartite Measures
Provides a theoretical criterion for multipartite entanglement classification, addressing a known bottleneck in quantum information theory.
The authors prove that third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states, and extend this to mixed states and multipartite qudit systems, with an application to conformal field theory.
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.