On the connection between the theorems of Gleason and of Kochen and Specker

Marzlin, Karl‐Peter; Landry, Taylor

doi:10.1139/cjp-2014-0631

Cited by 4 publications

(4 citation statements)

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“…The original KS theorem holds for vectors and defines a KS set as its constructive proof. On the other hand, Bell proved the so-called Bell theorem [75] as a corollary to the Gleason theorem [76] which is a projector formulation of the KS theorem [73,77]. Theorem 3.3.…”

Section: Theorem 32 Ks Mmp Hypergraphsmentioning

confidence: 99%

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: Theorem 32 Ks Mmp Hypergraphsmentioning

confidence: 99%

Quantum Contextuality

Pavičić

2023

Quantum

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“…The original KS theorem holds for vectors and defines a KS set as its constructive proof. On the other hand, Bell proved the so-called Bell theorem [71] as a corollary to the Gleason theorem [72] which is a projector formulation of the KS theorem [69,73].…”

Section: Extensions Of the Kochen-specker Theoremmentioning

confidence: 99%

Quantum Contextuality

Pavičić¹

2021

Preprint

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“…Gleason theorem had a major influence on Specker. It was actually shown that the Kochen-Specker theorem could be seen as a consequence of Gleason's: it constructs a finite set of rays on which no two-valued homomorphism exists, the existence of which is established by a simple extension to Gleason's theorem [93,94].…”

Section: The Gleason Theorem and Quantum Mechanics As A Prevision The...mentioning

confidence: 99%

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

Masse

2021

Preprint

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J. A tale of contextuality... K. ...and its logical implications III. Mathematical proofs of contextuality A. The Kochen-Specker Bell theorem B. KCBS inequality C. Peres-Mermin Square IV. The graph-theoretic approach of Cabello, Severini and Winter (CSW) A. General definitions B. The case of KCBS as a paradigmatic example C. Generalisation D. Link with Bell inequalities V. A sheaf-category theoretic approach to contextuality A. Pictorial representation 1. Probabilistic contextuality 2. Logical contextuality 3. Strong contextuality B. A brief presentation of the mathematical frameworks of the model 1. Correlation experiments in sheaf-theoretic approach 2. Compatibility of marginals 3. Hierarchy of contextuality C. New questions D. An illustration of contextuality VI. A hypergrah approach to contextuality VII. An operational version of contextuality A. A toy model B. An operational theory of contextuality C. Application to quantum mechanics D. Reinterpretation of the Kochen-Specker results VIII. Contextuality-by-Default A.

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On the connection between the theorems of Gleason and of Kochen and Specker

Cited by 4 publications

References 40 publications

Quantum Contextuality

Quantum Contextuality

Quantum Contextuality

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

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