title: Detection of multiparticle entanglement: quantifying the search for symmetric extensions.
abstract: We provide quantitative bounds on the characterization 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 norm induced by one-way local operations and classical communication, or in the Frobenius norm). Our results provide a theoretical justification for the use of the search for symmetric extensions as a test for multiparticle entanglement.
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8097 Zurich, Switzerland.
authors.forename: Fernando G S L
authors.initials: FG
authors.lastname: Brandão
authors.forename: Matthias
authors.initials: M
authors.lastname: Christandl