The rank of contextuality
| Autor: | Horodecki, Karol, Zhou, Jingfang, Stankiewicz, Maciej, Salazar, Roberto, Horodecki, Paweł, Raussendorf, Robert, Horodecki, Ryszard, Ramanathan, Ravishankar, Tyhurst, Emily |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | New J. Phys. 25 073003 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1367-2630/acdf78 |
| Popis: | 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. Comment: 15 pages, 5 figures |
| Databáze: | arXiv |
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