Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States Speaker(s): Elie Wolfe
Abstract: We present a method for determining the maximum possible violation of any linear Bell inequality per quantum mechanics. Essentially this amounts to a constrained optimization problem for an observable’s eigenvalues, but the problem can be reformulated so as to be analytically tractable. This opens the door for an arbitrarily precise characterization of quantum correlations, including allowing for nonrandom marginal expectation values. Such a characterization is critical when contrasting QM to superficially similar general probabilistic theories. We use such marginalinvolving quantum bounds to estimate the volume of all possible quantum statistics in the complete 8dimensional probability space of the BellCHSH scenario, measured relative to both local hidden variable models as well as general nosignaling theories. See arXiv:1106.2169. Time permitting, we’ll also discuss how one might go about trying to prove that a given mixed state is, in fact, not entangled. (The converse problem of certifying nonzero entanglement has received extensive treatment already.) Instead of directly asking if any separable representation exists for the state, we suggest simply checking to see if it “fits” some particular knownseparable form. We demonstrate how a surprisingly valuable sufficient separability criterion follows merely from considering a highlygeneric separable form. The criterion we generate for diagonallysymmetric mixed states is apparently completely tight, necessary and sufficient. We use integration to quantify the “volume” of states captured by our criterion, and show that it is as large as the volume of states associated with the PPT criterion; this simultaneously proves our criterion to be necessary as well as the PPT criterion to be sufficient, on this family of states. The utility of a sufficient separability criterion is evidenced by categorically rejecting Dickemodel superradiance for entanglement generation schema. See arXiv:1307.5779.
Date: 26/11/2013  3:30 pm
Series: Quantum Foundations
