Oded Regev (Tel Aviv University)
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.
NOTE: This talk requires absolutely no prior knowledge of quantum computation.
Joint work with Julia Kempe and Ben Toner