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arXiv · 1408.6829

Quantum de Finetti theorem under fully-one-way adaptive measurements

Ke Li·Graeme Smith
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Abstract

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully one-way LOCC (local operations and classical communication) measurements. Our result strengthens Brandão and Harrow's de Finetti theorem where a kind of partially one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.

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Ke Li, Graeme Smith. 2015-04-28. Quantum de Finetti theorem under fully-one-way adaptive measurements. https://doi.org/10.1103/physrevlett.114.160503

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