Geometric criterion for separability based on local measurement

TL;DR

This paper introduces a geometric criterion for quantum state separability based on local measurements, providing a new way to identify entanglement and measure it in multiparty quantum systems.

Contribution

It develops a geometric approach to determine separability of quantum states, including multiparty Werner states, and introduces a computable entanglement measure.

Findings

Separable states satisfy specific geometric constraints.

A separability criterion for multiparty Werner states is derived.

Distance from the normalized identity indicates separability for n-qudit systems.

Abstract

A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner states. It is demonstrated that separable states satisfy certain geometric constraints that entangled states do not. A separability criterion for multiparty Werner states of arbitrary dimension is derived. This approach can be used to determine separability across any bipartition of a general density matrix and leads naturally to a computable measure of entanglement for multiparty pure states. It is known that all density matrices within a certain distance of the normalized identity are separable. This distance is determined for a general setting of $n$ qudits, each of dimension $d$.