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The Unique Games Conjecture with Entangled Provers is False

Authors Julia Kempe, Oded Regev, Ben Toner

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  • Unique games
  • entanglement

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Abstract

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.

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Julia Kempe, Oded Regev, and Ben Toner. The Unique Games Conjecture with Entangled Provers is False. In Algebraic Methods in Computational Complexity. Dagstuhl Seminar Proceedings, Volume 7411, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/DagSemProc.07411.6

Author Details

Julia Kempe
Oded Regev
Ben Toner
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