Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces

Pavičić, Mladen; Megill, Norman D.

doi:10.1103/physreva.106.l060203

Cited by 3 publications

(13 citation statements)

References 19 publications

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“…To generate NBMMPHs in n-dim spaces we mostly rely on three methods-M1-M3 which make use of algorithms and programs developed in [58,41,60,46]. M1 consists in an automated dropping of vertices contained in single hyperedges (multiplicity m = 1; see Def.…”

Section: Methods Of Mmp Hypergraph Generationsmentioning

confidence: 99%

“…In a projector formulation, all KS MMP hypergraph with a coordinatization are stateindependent and for non-KS non-binary MMP hypergraphs one still has to find a general automated approach. However, in addition to numerous already known small non-KS nonbinary MMP hypergraphs [41] we do have an abundance of KS MMP hypergraphs of any size and structure in odd [46] and even [58,59,60] dimensional spaces.…”

Section: Methodsmentioning

confidence: 99%

“…We stress here, that for a k-l n-dim KS hypergraph in a general hypergraph representation, its incidence matrix contains k vertex rows each l columns long, while an MMP hypergraph is represented by a single line containing l n-tuples of vertices. E.g., the incidence matrix of the original 4-dim 192-118 Kochen-Specker hypergraph contains 118 hyperedge columns and 192 vertex rows/lines (192 × 118 matrix), while its single MMP string (one line) contains 118 triples of ASCII characters [46,Supp. Material].…”

Section: No Hyperedge Shares Only One Vertex With Another Hyperedge;mentioning

confidence: 99%

“…Renewed figures are given in the figure in Appendix B. New 3-dim MMP hypergraphs, mostly obtained in [46], are given in Fig. 10.…”

Section: -Dim Mmp Hypergraphsmentioning

confidence: 99%

“…Here we present a few examples from the 7-and 8-dim spaces. The distribution of the 7-dim KS MMP class is provided in [46] and of the 8-dim one in [58]. We give the structural properties of the examples in Table 9 and their ASCII strings and coordinatizations Appendix I.…”

Section: -Dim Ks Mmp Hypergraphs/setsmentioning

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: Methods Of Mmp Hypergraph Generationsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: No Hyperedge Shares Only One Vertex With Another Hyperedge;mentioning

confidence: 99%

“…Renewed figures are given in the figure in Appendix B. New 3-dim MMP hypergraphs, mostly obtained in [46], are given in Fig. 10.…”

Section: -Dim Mmp Hypergraphsmentioning

confidence: 99%

Section: -Dim Ks Mmp Hypergraphs/setsmentioning

confidence: 99%

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Quantum Contextuality

Pavičić

2023

Quantum

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Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications

Pavičić,

Waegell

2024

Phys. Rev. A

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Non-Kochen–Specker Contextuality

Pavičić

2023

Entropy

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Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen–Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods—whose complexity does not scale up with the dimension—for generating such non-Kochen–Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.

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Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces

Cited by 3 publications

References 19 publications

Quantum Contextuality

Quantum Contextuality

Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications

Non-Kochen–Specker Contextuality

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