  We establish the first hardness results for the problem of computing the
value of one-round games played by a verifier and a team of provers 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 verifier and two entangled provers or (ii) classical verifier and three
entangled provers. 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-prover
games to make them resistant to entangled provers. 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 P=NP, the values of entangled-prover games cannot be
computed by semidefinite programs that are polynomial in the size of the
verifier's system, a method that has been successful for more restricted
quantum games.
