"""
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* contains 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, and are thus restricted to being quasi-classical.
"""
MIP = Multi-prover Interactive Proof, a class of languages, is known to be equivalent to NEXP, (the class containing all languages computable in exponential time by a machine operating in a non-deterministic fashion [eg. the ones you care about]).
MIP* is like MIP except the provers (the M) are allowed to communicate with each other using quantum entanglement. This type of communication would be undetectable by the questioner (the verifier) and thus allow a group of attackers to "cheat" various cryptographic protocols. However, it is found that MIP* contains MIP. Therefore, there are proof systems (and thus protocols) resistant to quantum communication of the provers.
Thus, zero-knowledge proofs and the like still work in with quantum entanglement powered assailants.
""" 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* contains 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, and are thus restricted to being quasi-classical. """
(I have no idea what that means.)