Parallel repetition of entangled games

Julia Kempe, Thomas Vidick

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the number of rounds or the number of players? Classically, efforts to resolve this question, open for many years, have culminated in Raz's celebrated parallel repetition theorem on one hand, and in efficient product testers for PCPs on the other. In the case where players share entanglement, the only previously known results are for special cases of games, and are based on techniques that seem inherently limited. Here we show for the first time that the maximum success probability of entangled games can be reduced through parallel repetition, provided it was not initially 1. Our proof is inspired by a seminal result of Feige and Kilian in the context of classical two-prover one-round interactive proofs. One of the main components in our proof is an orthogonalization lemma for operators, which might be of independent interest.

Original languageEnglish (US)
Title of host publicationSTOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing
Pages353-362
Number of pages10
DOIs
StatePublished - Jul 4 2011
Event43rd ACM Symposium on Theory of Computing, STOC'11 - San Jose, CA, United States
Duration: Jun 6 2011Jun 8 2011

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other43rd ACM Symposium on Theory of Computing, STOC'11
CountryUnited States
CitySan Jose, CA
Period6/6/116/8/11

Keywords

  • entangled games
  • parallel repetition

ASJC Scopus subject areas

  • Software

Cite this

Kempe, J., & Vidick, T. (2011). Parallel repetition of entangled games. In STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing (pp. 353-362). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1993636.1993684