Journal article · Preprint article
Perfect Strategies for Non-Local Games
California Institute of Technology1
Autonomous University of Barcelona2
University of Copenhagen3
University of Waterloo4
Quantum Physics and Information Technology, Department of Physics, Technical University of Denmark5
Department of Physics, Technical University of Denmark6
Technical University of Denmark7
Universidad Politécnica de Madrid8
University College London9
Queen's University Belfast10
...and 0 moreWe 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.
Language: | English |
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Publisher: | Springer Netherlands |
Year: | 2020 |
Journal subtitle: | An International Journal Devoted To the Theory and Applications of Analysis and Geometry To Physics |
ISSN: | 15729656 and 13850172 |
Types: | Journal article and Preprint article |
DOI: | 10.1007/s11040-020-9331-7 |
ORCIDs: | Roberson, D.E. and 0000-0001-9727-4961 |