License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.07411.6
URN: urn:nbn:de:0030-drops-13048
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Kempe, Julia ; Regev, Oded ; Toner, Ben

The Unique Games Conjecture with Entangled Provers is False

07411.RegevOded.Paper.1304.pdf (0.5 MB)


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.

BibTeX - Entry

  author =	{Kempe, Julia and Regev, Oded and Toner, Ben},
  title =	{{The Unique Games Conjecture with Entangled Provers is False}},
  booktitle =	{Algebraic Methods in Computational Complexity},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7411},
  editor =	{Manindra Agrawal and Harry Buhrman and Lance Fortnow and Thomas Thierauf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-13048},
  doi =		{10.4230/DagSemProc.07411.6},
  annote =	{Keywords: Unique games, entanglement}

Keywords: Unique games, entanglement
Collection: 07411 - Algebraic Methods in Computational Complexity
Issue Date: 2008
Date of publication: 15.01.2008

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