Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2011.06508

Three noncontextual hidden variable models for the Peres-Mermin square

Gábor Hofer‐Szabó

Published Nov 1, 2020• 8 citations
arXivHTMLPDF

Abstract

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).

Related papers

Sequential measurements and the Kochen-Specker arguments

Gábor Hofer‐Szabó

It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres-Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

arXiv:2305.16902•May 26, 2023•0 citations

Quantum contextuality in the Mermin-Peres square: A hidden-variable perspective

Brian R. La Cour

The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden-variable theory. It is shown that such a hidden-variable description can be viewed as either contextual in the random variables mapping hidden states to observable outcomes or in the probability measure on the hidden state space. The latter view suggests that this apparent contextuality may be interpreted as a simple consequence of measurement disturbance, wherein the initial hidden state is altered through interaction with the measuring device, thereby giving rise to a possibly different final hidden-variable state from which the measurement outcome is obtained. In light of this observation, a less restrictive and, arguably, more reasonable definition of noncontextuality is suggested. To prove that such a description is possible, an explicit and, in this sense, noncontextual hidden-variable model is constructed, which reproduces all quantum theoretic predictions for the Mermin-Peres square. A critical analysis of some recent and proposed experimental tests of contextuality is also provided. Although the discussion is restricted to a four-dimensional Hilbert space, the approach and conclusions are expected to generalize to any Hilbert space.

arXiv:2105.00940•Physical Review A•Jan 5, 2009•23 citations

Quantum Contextuality as a Measurement Disturbance Effect

Brian R. La Cour, Luigi Accardi, Guillaume Adenier +5 more

The question of quantum contextuality in the Mermin‐Peres square is considered. It is shown that a deterministic, noncontextual hidden variable model of this problem is not inconsistent with quantum mechanics, contrary to the Kochen‐Specker theorem. The key idea is that measurement outcomes may be viewed as deterministic functions of hidden variable states which are disturbed through the process of measurement. This, in turn, implies that the outcome of measuring the product of two commensurate observables need not be equal to the product of the outcomes that would have been obtained had they been measured individually. A critical analysis of some recent and proposed experimental tests of contextuality is also provided.

AIP conference proceedings•Jan 1, 2009•0 citations

Measuring the Mermin-Peres magic square using an online quantum computer

Altay Dikme, N. Reichel, Amine Laghaout +1 more

We have implemented the six series of three commuting measurement of the Mermin-Peres magic square on an online, five qubit, quantum computer. The magic square tests if the measurements of the system can be described by physical realism (in the EPR sense) and simultaneously are non-contextual. We find that our measurement results violate any realistic and non-contextual model by almost 28 standard deviations. We also find that although the quantum computer we used for the measurements leaves much to be desired in producing accurate and reproducible results, the simplicity, the ease of re-running the measurement programs, and the user friendliness compensates for this fact.

arXiv:2009.10751•Sep 22, 2020•4 citations

Violating noncontextual realism through sequential measurements

Jan-Åke Larsson, Matthias Kleinmann, Otfried Gühne +1 more

The question of whether noncontextual hidden variable models can give the quantum‐mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden‐variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible.

AIP conference proceedings•Jan 1, 2011•6 citations

Violating noncontextual realism through sequential measurements

Jan-Åke Larsson, Matthias Kleinmann, Otfried Gühne +5 more

The question of whether noncontextual hidden variable models can give the quantum‐mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden‐variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible.

AIP conference proceedings•Jan 1, 2011•3 citations
I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).
It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres-Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.
The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden-variable theory. It is shown that such a hidden-variable description can be viewed as either contextual in the random variables mapping hidden states to observable outcomes or in the probability measure on the hidden state space. The latter view suggests that this apparent contextuality may be interpreted as a simple consequence of measurement disturbance, wherein the initial hidden state is altered through interaction with the measuring device, thereby giving rise to a possibly different final hidden-variable state from which the measurement outcome is obtained. In light of this observation, a less restrictive and, arguably, more reasonable definition of noncontextuality is suggested. To prove that such a description is possible, an explicit and, in this sense, noncontextual hidden-variable model is constructed, which reproduces all quantum theoretic predictions for the Mermin-Peres square. A critical analysis of some recent and proposed experimental tests of contextuality is also provided. Although the discussion is restricted to a four-dimensional Hilbert space, the approach and conclusions are expected to generalize to any Hilbert space.
The question of quantum contextuality in the Mermin‐Peres square is considered. It is shown that a deterministic, noncontextual hidden variable model of this problem is not inconsistent with quantum mechanics, contrary to the Kochen‐Specker theorem. The key idea is that measurement outcomes may be viewed as deterministic functions of hidden variable states which are disturbed through the process of measurement. This, in turn, implies that the outcome of measuring the product of two commensurate observables need not be equal to the product of the outcomes that would have been obtained had they been measured individually. A critical analysis of some recent and proposed experimental tests of contextuality is also provided.
We have implemented the six series of three commuting measurement of the Mermin-Peres magic square on an online, five qubit, quantum computer. The magic square tests if the measurements of the system can be described by physical realism (in the EPR sense) and simultaneously are non-contextual. We find that our measurement results violate any realistic and non-contextual model by almost 28 standard deviations. We also find that although the quantum computer we used for the measurements leaves much to be desired in producing accurate and reproducible results, the simplicity, the ease of re-running the measurement programs, and the user friendliness compensates for this fact.
The question of whether noncontextual hidden variable models can give the quantum‐mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden‐variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible.
The question of whether noncontextual hidden variable models can give the quantum‐mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden‐variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible.