Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

TL;DR

This paper introduces entanglement polytopes, geometric tools that allow the characterization of global multi-particle entanglement using only local single-particle information in pure states, simplifying entanglement detection.

Contribution

It presents a novel geometric framework, entanglement polytopes, enabling the identification of multi-particle entanglement from local data in pure states, applicable to arbitrary system sizes.

Findings

Entanglement polytopes characterize global entanglement from local information.

Local witnesses for entanglement are derived from the polytopes.

Method extends to noisy states with low noise levels.

Abstract

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure multi-particle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating with any given class of entanglement an entanglement polytope---a geometric object which characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement, and can be generalized to states affected by low levels of noise.