SYNCHRONOUS GAMES WITH *-ISOMORPHIC GAME ALGEBRAS

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1 Scopus citations

Abstract

We establish several strong equivalences of synchronous non-local games, in the sense that the corresponding game algebras are ∗-isomorphic. We first show that the game algebra of any synchronous game on n inputs and k outputs is ∗-isomorphic to the game algebra of an associated bisynchronous game on nk inputs and nk outputs. As a result, we show that there are bisynchronous games with equal question and answer sets, whose optimal strategies only exist in the quantum commuting model, and not in the quantum approximate model. Moreover, we show that there are bisynchronous games with equal question and answer sets that have non-zero game algebras, but no winning quantum commuting strategies, resolving a problem of V.I. Paulsen and M. Rahaman. We also exhibit a ∗-isomorphism between any synchronous game algebra with n questions and k > 3 answers and a synchronous game algebra with n(k − 2) questions and 3 answers.

Original languageEnglish (US)
Pages (from-to)924-946
Number of pages23
JournalQuantum Information and Computation
Volume22
Issue number11-12
DOIs
StatePublished - Aug 2022
Externally publishedYes

Keywords

  • bisynchronous game
  • game algebra
  • synchronous game

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Computational Theory and Mathematics

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