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Perfect strategies for non-signalling games

Lupini, M. and Mančinska, L. and Paulsen, V. I. and Roberson, D. E. and Scarpa, G. and Severini, S. and Todorov, I. G. and Winter, A. (2020) Perfect strategies for non-signalling games. Mathematical Physics, Analysis and Geometry, 23 . Art. No. 7. ISSN 1385-0172.

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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.

Item Type:Article
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Lupini, M.0000-0003-1588-7057
Additional Information:© 2020 Springer Nature Switzerland AG. Received 29 July 2019; Accepted 20 January 2020; Published 26 February 2020. Part of this research was conducted during two Focused Research Meetings, funded by the Heilbronn Institute, and hosted at Queen’s University Belfast in October 2016 and March 2017. M. Lupini was partially supported by the NSF grant DMS-1600186. G. Scarpa acknowledges the support of MTM2014-54240-P (MINECO), QUITEMAD+-CM Reference: S2013/ICE-2801 (Comunidad de Madrid), ICMAT Severo Ochoa project SEV-2015-0554 (MIN-ECO), and grant 48322 from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.
Funding AgencyGrant Number
Heilbronn InstituteUNSPECIFIED
Ministerio de Economía, Industria y Competitividad (MINECO)MTM2014-54240-P
Comunidad de MadridS2013/ICE-2801
Severo OchoaSEV-2015-0554
John Templeton Foundation48322
Record Number:CaltechAUTHORS:20190205-103045491
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Official Citation:Lupini, M., Mančinska, L., Paulsen, V.I. et al. Perfect Strategies for Non-Local Games. Math Phys Anal Geom 23, 7 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92664
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 18:58
Last Modified:09 Mar 2020 13:19

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