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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. (2018) Perfect strategies for non-signalling games. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20190205-103045491

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Abstract

We unify and consolidate various results about non-signalling games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a number of known facts in a variety of special cases. Among these families are reflexive games, which are characterised as the hardest non-signalling games that can be won using a given set of strategies. We introduce it imitation games, in which the players display linked behaviour, and which contains as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and it 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, extending known results about synchronous games. We single out a subclass of imitation games, which we call it 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. We describe the main classes of non-signalling correlations in terms of states on operator system tensor products.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1804.06151arXivDiscussion Paper
Additional Information: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. 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 (MINECO), 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.
Funders:
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 Foundation4832
Record Number:CaltechAUTHORS:20190205-103045491
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190205-103045491
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92664
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 18:58
Last Modified:03 Oct 2019 20:46

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