New Journal of Physics (Jan 2023)

The rank of contextuality

  • Karol Horodecki,
  • Jingfang Zhou,
  • Maciej Stankiewicz,
  • Roberto Salazar,
  • Paweł Horodecki,
  • Robert Raussendorf,
  • Ryszard Horodecki,
  • Ravishankar Ramanathan,
  • Emily Tyhurst

DOI
https://doi.org/10.1088/1367-2630/acdf78
Journal volume & issue
Vol. 25, no. 7
p. 073003

Abstract

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Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.

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