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Title:
A Multi-Prover Interactive proof for NEXP Sound Against Entangled Provers
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Abstract:
We prove a strong limitation on the ability of entangled provers to collude in a multiplayer game. Our main result is the first nontrivial lower bound on the class MIP* of languages having multi-prover interactive proofs with entangled provers; namely MIP* contains NEXP, the class of languages decidable in non-deterministic exponential time. While Babai, Fortnow, and Lund (Computational Complexity 1991) proved the celebrated equality MIP=NEXP in the absence of entanglement, ever since the introduction of the class MIP* it was open whether shared entanglement between the provers could weaken or strengthen the computational power of multi-prover interactive proofs. Our result shows that it does not weaken their computational power: MIP \subseteq MIP*.At the heart of our result is a proof that Babai, Fortnow, and Lund's ``multilinearity test’’ is sound even in the presence of entanglement between the provers, and our analysis of this test could be of independent interest. As a byproduct we show that the correlations produced by any entangled strategy which succeeds in the multilinearity test with high probability can always be closely approximated using shared randomness alone.This is a joint work with Thomas Vidick. A paper is available at http://arxiv.org/abs/1207.0550.
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