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Faithful squashed entanglement with applications to separability testing and quantum complexity

Jon Yard, Los Alamos National Laboratory

(Session 4 : Friday from 2:30pm-3:00pm)

Abstract. Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this talk, I will present a new lower bound for squashed entanglement in terms of the distance to the set of separable states, along with several applications. I will first show how this implies that squashed entanglement is a faithful measure of entanglement, meaning it is positive on a state if and only if it is entangled. The bound also implies a new de Finetti-type bound for quantum states which, in turn, implies a quasipolynomial-time algorithm for deciding if a density matrix is entangled. The best known algorithms for this problem had been exponential. I will also show several applications in quantum complexity theory by giving new multi-prover characterizations of QMA, which is a quantum analog of NP. The bound follows from a sequence of new results about entanglement measures, whose proofs utilize some recent results in quantum information theory. These include an operational interpretation of quantum conditional mutual information as the optimal communication rate in quantum state redistribution, and an operational interpretation of the regularized relative entropy of entanglement as the optimal error rate for hypothesis testing with one-sided error. Another crucial aspect of the proof is the utilization of operationally-motivated norms on bipartite states that quantify distinguishability under local operations and classical communication. This is joint work (arXiv:1010.1750, 1011.2751) with Fernando Brandão and Matthias Christandl.