Rank of contextuality

ORAL

Abstract

We propose a new measure of statistical Kochen-Specker contextuality, called rank of contextuality. The rank of contextuality is the minimal number of noncontextual boxes (input-output devices admitting a non-contextual hidden variable model) that are needed to switch between in order to simulate a contextual box. We show that the logarithm of the rank of contextuality is additive, faithful measure of contextuality, monotonous under simple wirings. We also provide a construction of contextual boxes with arbitrary high rank of contextuality, exhibiting thereby extremely high logical contradiction.

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Presenters

  • Jingfang Zhou

    • University of Tokyo

Authors

  • Karol Horodecki

    • Institute of Informatics, National Quantum Information Centre, Department of Physics, Mathematics and Informatics, University of Gdansk

  • Jingfang Zhou

    • University of Tokyo

  • Pawel Horodecki

    • Faculty of Applied Physics and Mathematics, Gdansk University of Technology

  • Robert Raussendorf

    • Department of Physics & Astronomy, University of British Columbia

  • Ryszard Horodecki

    • Faculty of Applied Physics and Mathematics, National Quantum Information Centre, Gdansk University of Technology

  • Ravishankar Ramanathan

    • Laboratoire d ’Information Quantique, Universite Libre de Bruxelles

  • Emily Tyhurst

    • University of Toronto