We consider one-round games between a classical verifier and two
provers who share entanglement. We show that when the constraints
enforced by the verifier are 'unique' constraints (i.e.,
permutations), the value of the game can be well approximated by a
semidefinite program. Essentially the only algorithm known
previously was for the special case of binary answers, as follows
from the work of Tsirelson in 1980. Among other things, our result
implies that the variant of the unique games conjecture where we
allow the provers to share entanglement is false. Our proof is
based on a novel 'quantum rounding technique', showing how to take
a solution to an SDP and transform it to a strategy for entangled
provers.