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Bisynchronous Games and Factorizable Maps

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Abstract

We introduce a new class of non-local games and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop a close connection between these non-local games and the theory of quantum groups which recently surfaced in studies of graph isomorphism games. When the number of inputs is equal to the number of outputs, we prove that a bisynchronous density arises from a trace on the quantum permutation group. Each bisynchronous density gives rise to a completely positive map, and we prove that these maps are factorizable maps.

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Acknowledgements

This work was done while MR was a Postdoctoral Fellow at the department of Pure Mathematics, University of Waterloo.

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Authors and Affiliations

  1. Institute for Quantum Computing and Department of Pure Mathematics, University of Waterloo, Waterloo, ON , N2L 3G1, Canada

    Vern I. Paulsen

  2. Department of Mathematics, BITS Pilani K.K Birla Goa Campus, Sancoale, Goa , 403726, India

    Mizanur Rahaman

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  1. Vern I. Paulsen
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  2. Mizanur Rahaman
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Correspondence to Mizanur Rahaman.

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Communicated by Matthias Christandl.

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Paulsen, V.I., Rahaman, M. Bisynchronous Games and Factorizable Maps. Ann. Henri Poincaré 22, 593–614 (2021). https://doi.org/10.1007/s00023-020-01003-2

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  • DOI: https://doi.org/10.1007/s00023-020-01003-2

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