title: Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements.
abstract: 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 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 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.
authors.affiliation: IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA.|Center for Theoretic Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Ke
authors.initials: K
authors.lastname: Li
authors.affiliation: IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA.
authors.forename: Graeme
authors.initials: G
authors.lastname: Smith