# Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces

@article{Pavicic2018VectorGO, title={Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces}, author={Mladen Pavicic and Norman D. Megill}, journal={Entropy}, year={2018}, volume={20} }

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…

## 9 Citations

Automated generation of Kochen-Specker sets

- Computer ScienceScientific Reports
- 2019

Methods and algorithms that are applied to downward generation of Kochen-Specker master sets obtained from a small number of simple vector components that can overcome the exponential barrier in many cases of interest are presented.

Hypergraph Contextuality

- Computer ScienceEntropy
- 2019

This paper presents a third, hypergraph-based class of contextual sets, the simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation and enabling establishing new entropic contextualities.

Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability

- Philosophy
- 2021

In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically, those structures serve…

Hardy-type "proofs" or paradoxes as true-implies-false gadgets

- Philosophy
- 2020

Hardy-type arguments are presented uniformly by enumerating the orthogonality hypergraphs that underly their structure. The resulting collection of observables, if interpreted classically, induce a…

Decomposability versus entanglement of quantum states in four dimensions bound by pre-selection of two-dimensional subspaces

- Mathematics
- 2020

Criteria for the completion of a given incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are specified.

Generalized Householder Transformations

- MathematicsEntropy
- 2022

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. The dichotomy is modulated by…

Completing bases in four dimensions

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

Criteria and constructive methods for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.

ph ] 1 5 N ov 2 01 9 Hypergraph

- Computer Science
- 2019

This paper presents a third, hypergraph-based class of contextual sets, the simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation and enabling establishing new entropic contextualities.

Quantum Probability and Randomness

- Computer ScienceEntropy
- 2019

The recent quantum information revolution has stimulated interest in the quantum foundations by perceiving and re-evaluating the theory from a novel information-theoretical viewpoint [...].

## References

SHOWING 1-10 OF 65 REFERENCES

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

- Computer Science
- 2017

An arbitrary exhaustive hypergraph-based generation of the most explored contextual sets---Kochen-Specker (KS) ones---in 4, 6, 8, 16, and 32 dimensions with MMP hypergraph language, algorithms, and programs is presented.

Contextuality supplies the ‘magic’ for quantum computation

- PhysicsNature
- 2014

This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer.

Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem

- Physics
- 2014

For eight-dimensional quantum systems there is a Kochen-Specker (KS) set of 40 quantum yes-no tests that is related to the Greenberger-Horne-Zeilinger (GHZ) proof of Bell's theorem. Here we…

Contextuality for preparations, transformations, and unsharp measurements

- Philosophy
- 2005

The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an…

Graph approach to quantum systems

- Mathematics
- 2010

Using a graph approach to quantum systems, we show that descriptions of 3-dim Kochen–Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie diagrams (a kind of…

Applying the simplest Kochen-Specker set for quantum information processing.

- PhysicsPhysical review letters
- 2014

An input state-independent experimental technique is reported to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.

Kochen-Specker set with seven contexts

- Mathematics
- 2014

The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsets…

On small proofs of the Bell-Kochen-Specker theorem for two, three and four qubits

- Mathematics
- 2012

The Bell-Kochen-Specker (BKS) theorem rules out realistic non-contextual theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the…