The unique games conjecture with entangled provers is false
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.
|Dagstuhl Seminar Proceedings|
|Quantum Information Processing|
|Algebraic Methods in Computational Complexity, 2007|
|Organisation||Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands|
Kempe, J. (Julia), Regev, O, & Toner, B.F. (2008). The unique games conjecture with entangled provers is false. In Dagstuhl Seminar Proceedings. doi:10.4230/DagSemProc.07411.6