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DAGSTUHL
2007

The Unique Games Conjecture with Entangled Provers is False

13 years 5 months ago
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.
Julia Kempe, Oded Regev, Ben Toner
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Where DAGSTUHL
Authors Julia Kempe, Oded Regev, Ben Toner
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