Tsirelson Polytopes and Randomness Generation

ORAL

Abstract

We classify the extreme points of polytopes of probability distributions in the (2,2,2) Bell-CHSH setting that are induced by a single Tsirelson bound. We also do the same for a parametrized family of polytopes obtained from two Tsirelson bounds that interact non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (PRA 98:040304(R) (2018), arXiv:1812.07786, arXiv:1806.04553). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.

*This work was partially supported by NSF grant number 1839223 and Louisiana Board of Regents contract number LEQSF(2019-22)-RD-A-27.

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Presenters

  • Peter Bierhorst

    • Mathematics, University of New Orleans

Authors

  • Peter Bierhorst

    • Mathematics, University of New Orleans

  • Yanbao Zhang

    • NTT Corporation

  • Emanuel H Knill

    • NIST
    • National Institute of Standards and Technology