Kochen–Specker Sets and Generalized Orthoarguesian Equations

Megill, Norman D.; Pavičić, Mladen

doi:10.1007/s00023-011-0109-0

Cited by 10 publications

(16 citation statements)

References 16 publications

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“…Recently, quantum contextuality found applications in quantum communication [ 1 , 2 ], quantum computation [ 3 , 4 ], quantum nonlocality [ 5 ] and lattice theory [ 6 , 7 ]. This has prompted experimental implementation with photons [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], classical light [ 20 , 21 , 22 , 23 ], neutrons [ 24 , 25 , 26 ], trapped ions [ 27 ], solid state molecular nuclear spins [ 28 ] and superconducting quantum systems [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Hypergraph Contextuality

Pavičić

2019

Entropy

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Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, i.e., sets of quantum observables capable to reveal quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets: the Kochen-Specker ones and the operatorbased ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities.

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Section: Introductionmentioning

confidence: 99%

Hypergraph Contextuality

Pavičić

2019

Entropy

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“…[1,2] The most recent result of A. Cabello [3], according to which local contextuality can be used to reveal quantum nonlocality, supports this conjecture. Also our most recent results [4,5,6] show that KS sets play an important role in Hilbert space description of complex setups.…”

Section: Introductionmentioning

confidence: 79%

Probabilistic generation of quantum contextual sets

Megill¹,

Fresl²,

Waegell³

et al. 2011

Physics Letters A

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We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. Using a random sample of the sets generated with our method, we give a statistical estimate of the number of sets that might be obtained in an eventual exhaustive enumeration.

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“…It stems directly from the representation of KS configuration with MMP hypergraphs. Notice that the

-feature precludes interpretation of practically any KS hypergraph in an even dimensional Hilbert space by means of so-called Greechie diagrams, which by definition require that two blocks (similar to hypergraph edges) do not share more than one atom (similar to a vertex) [ 6 ], on the one hand, and that the loops made by the blocks must be of order five or higher (which is hardly ever realised in even dimensional KS hypergraphs—see examples in [ 37 ]), on the other.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, it has been discovered that quantum contextuality might have a significant place in a development quantum communication [ 1 , 2 ], quantum computation [ 3 , 4 ], and lattice theory [ 5 , 6 ]. This has prompted experimental implementation of 4-, 6-, and 8-dimensional contextual experiments with photons [ 7 , 8 , 9 , 10 , 11 , 12 , 13 ], neutrons [ 14 , 15 , 16 ], trapped ions [ 17 ], solid state molecular nuclear spins [ 18 ], and paths [ 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces

Pavičić

Megill

2018

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Recently, quantum contextuality has been proved to be the source of quantum computation's power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their features. The most elaborated contextual sets, which offer blueprints for contextual experiments and computational gates, are the Kochen-Specker (KS) sets. In this paper, we show a method of vector generation that supersedes previous methods. It is implemented by means of algorithms and programs that generate hypergraphs embodying the Kochen-Specker property and that are designed to be carried out on supercomputers. We show that vector component generation of KS hypergraphs exhausts all possible vectors that can be constructed from chosen vector components, in contrast to previous studies that used incomplete lists of vectors and therefore missed a majority of hypergraphs. Consequently, this unified method is far more efficient for generations of KS sets and their implementation in quantum computation and quantum communication. Several new KS classes and their features have been found and are elaborated on in the paper. Greechie diagrams are discussed. A detailed and complete blueprint of a particular 21-11 KS set with a complex coordinatization is presented in Appendix A, in contrast to the one from the published version of this paper where only a few of its states were given.

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Kochen–Specker Sets and Generalized Orthoarguesian Equations

Cited by 10 publications

References 16 publications

Hypergraph Contextuality

Hypergraph Contextuality

Probabilistic generation of quantum contextual sets

Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces

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