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FOCS
2008
IEEE

Unique Games with Entangled Provers are Easy

14 years 5 months ago
Unique Games with Entangled Provers are Easy
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. Using our approximation by a semidefinite program we also show a parallel repetition theorem for unique entangled games.
Julia Kempe, Oded Regev, Ben Toner
Added 29 May 2010
Updated 29 May 2010
Type Conference
Year 2008
Where FOCS
Authors Julia Kempe, Oded Regev, Ben Toner
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