Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements
Author(s)
Li, Ke; Smith, Graeme
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We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandao 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 an 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.
Date issued
2015-04Department
Massachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Laboratory for Nuclear ScienceJournal
Physical Review Letters
Publisher
American Physical Society
Citation
Li, Ke, and Graeme Smith. “Quantum de Finetti Theorem Under Fully-One-Way Adaptive Measurements.” Physical Review Letters 114, no. 16 (April 2015). © 2015 American Physical Society
Version: Final published version
ISSN
0031-9007
1079-7114