The rank of contextuality

Horodecki, Karol; Zhou, Jingfang; Stankiewicz, M. A.; Salazar, Roberto; Horodecki, Paweł; Raussendorf, Robert; Horodecki, Ryszard; Ramanathan, Ravishankar; Tyhurst, Emily

doi:10.48550/arxiv.2205.10307

Cited by 1 publication

(2 citation statements)

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“…It seems to us that l cm is the "rank of contextuality" Horodecki at al. [85] introduced as a quantifier of contextuality for hypergraphs, although it is rather difficult to establish a correspondence between their formalism and the MMP hypergraph language, in particular because they keep using several different names for vertices and hyperedges throughout their paper. Whenever we refer to both e M ax -and e min -inequalities we invoke them as e-inequalities.…”

Section: Postprocessed Data Statistics Takes Into Account That Within...mentioning

confidence: 99%

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Quantum Contextuality

Pavičić

2023

Quantum

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Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their structures and properties. Such engineering and subsequent implementation rely on discrimination between statistics of measurement data of quantum states and those of their classical counterparts. The discriminators considered are inequalities defined for hypergraphs whose structure and generation are determined by their basic properties. The generation is inherently random but with the predetermined quantum probabilities of obtainable data. Two kinds of statistics of the data are defined for the hypergraphs and six kinds of inequalities. One kind of statistics, often applied in the literature, turn out to be inappropriate and two kinds of inequalities turn out not to be noncontextuality inequalities. Results are obtained by making use of universal automated algorithms which generate hypergraphs with both odd and even numbers of hyperedges in any odd and even dimensional space – in this paper, from the smallest contextual set with just three hyperedges and three vertices to arbitrarily many contextual sets in up to 8-dimensional spaces. Higher dimensions are computationally demanding although feasible.

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Section: Postprocessed Data Statistics Takes Into Account That Within...mentioning

confidence: 99%

“…We conjecture that l cm is the "rank of contextuality" recently introduced by Horodecki at al. [85].…”

Section: Operator-based Vs Mmp-hypergraph-based Contextualitymentioning

confidence: 99%