Unique games with entangled provers are easy

Julia Kempe, Oded Regev, Ben Toner

Research output: Contribution to journalArticlepeer-review


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 (SDP). 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 into a strategy for entangled provers. Using our approximation by an SDP, we also show a parallel repetition theorem for unique entangled games.

Original languageEnglish (US)
Pages (from-to)3207-3229
Number of pages23
JournalSIAM Journal on Computing
Issue number7
StatePublished - 2010


  • Parallel repetition
  • Quantum entanglement
  • Semidefinite programming
  • Two-prover one-round games

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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