Polynomial-space approximation of no-signaling provers
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Unique Games with Entangled Provers Are Easy
SIAM Journal on Computing
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
A lower bound on the value of entangled binary games
Quantum Information & Computation
Entanglement-resistant two-prover interactive proof systems and non-adaptive pir's
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Nonlocal quantum XOR games for large number of players
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Classical, quantum and nonsignalling resources in bipartite games
Theoretical Computer Science
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We establish the first hardness results for the problem of computing the value of one-round games played by a referee and a team of players who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within an inverse polynomial the value of a one-round game with (i) quantum referee and two entangled players or (ii) classical referee and three entangled players. Previously it was not even known if computing the value exactly is \NP-hard. We also describe a mathematical conjecture, which, if true, would imply hardness of approximation to within a constant.We start our proof by describing two ways to modify classical multi-player games to make them resistant to entangled players. We then show that a strategy for the modified game that uses entanglement can be ``rounded'' to one that does not. The results then follow from classical inapproximability bounds. Our work implies that, unless $\Pe=\NP$, the values of entangled-player games cannot be computed by semidefinite programs that are polynomial in the size of the referee's system, a method that has been successful for more restricted quantum games.