Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions

TL;DR

This paper establishes quantitative bounds for detecting multiparticle entanglement using symmetric extensions, providing theoretical support for a practical entanglement detection method with algorithmic applications.

Contribution

It introduces bounds relating multiparticle separability to symmetric extensions, justifies their use in entanglement detection, and presents a quasipolynomial-time algorithm for testing separability.

Findings

Quantitative bounds on multiparticle separability

Algorithmic method for entanglement detection

Theoretical support for symmetric extension tests

Abstract

We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of de Finetti's theorem. We discuss algorithmic applications of our results, in particular a quasipolynomial-time algorithm to decide whether a multiparticle quantum state is separable or entangled (for constant number of particles and constant error in the LOCC or Frobenius norm). Our results provide a theoretical justification for the use of the Search for Symmetric Extensions as a practical test for multiparticle entanglement.