The rank of contextuality

Research output: Contribution to journalArticleResearchpeer review

Authors

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

External Research Organisations

  • University of Gdansk
  • University of Tokyo
  • Jagiellonian University
  • Gdansk University of Technology
  • University of British Columbia
  • The University of Hong Kong
  • University of Toronto
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Details

Original languageEnglish
Article number073003
JournalNew journal of physics
Volume25
Issue number7
Publication statusPublished - 10 Jul 2023
Externally publishedYes

Abstract

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.

Keywords

    contextuality, nonlocality, quantum

ASJC Scopus subject areas

Cite this

The rank of contextuality. / Horodecki, Karol; Zhou, Jingfang; Stankiewicz, Maciej et al.
In: New journal of physics, Vol. 25, No. 7, 073003, 10.07.2023.

Research output: Contribution to journalArticleResearchpeer review

Horodecki, K, Zhou, J, Stankiewicz, M, Salazar, R, Horodecki, P, Raussendorf, R, Horodecki, R, Ramanathan, R & Tyhurst, E 2023, 'The rank of contextuality', New journal of physics, vol. 25, no. 7, 073003. https://doi.org/10.1088/1367-2630/acdf78
Horodecki, K., Zhou, J., Stankiewicz, M., Salazar, R., Horodecki, P., Raussendorf, R., Horodecki, R., Ramanathan, R., & Tyhurst, E. (2023). The rank of contextuality. New journal of physics, 25(7), Article 073003. https://doi.org/10.1088/1367-2630/acdf78
Horodecki K, Zhou J, Stankiewicz M, Salazar R, Horodecki P, Raussendorf R et al. The rank of contextuality. New journal of physics. 2023 Jul 10;25(7):073003. doi: 10.1088/1367-2630/acdf78
Horodecki, Karol ; Zhou, Jingfang ; Stankiewicz, Maciej et al. / The rank of contextuality. In: New journal of physics. 2023 ; Vol. 25, No. 7.
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abstract = "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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