Perfect Strategies for Non-Local Games

M. Lupini*, L. Mančinska, V. I. Paulsen, D.E. Roberson, G. Scarpa, S. Severini, I. G. Todorov, A. Winter

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C∗(G) to any imitation game G, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G can be characterised in terms of properties of this C*-algebra. We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra.
Original languageEnglish
Article number7
JournalMathematical Physics Analysis and Geometry
Volume23
Issue number1
Number of pages31
ISSN1572-9656
DOIs
Publication statusPublished - 2020

Keywords

  • Non-local game
  • Imitation game
  • Perfect strategy

Cite this

Lupini, M., Mančinska, L., Paulsen, V. I., Roberson, D. E., Scarpa, G., Severini, S., Todorov, I. G., & Winter, A. (2020). Perfect Strategies for Non-Local Games. Mathematical Physics Analysis and Geometry, 23(1), [7]. https://doi.org/10.1007/s11040-020-9331-7