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

The problem of contextuality and the impossibility of experimental metaphysics thereof

Ronnie Hermens

Published Jan 1, 2011• 18 citations
OpenAlex

Abstract

Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen-Specker Theorem. Although we disagree with this last statement, the models play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality --with an emphasis on operational definitions-- and argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.

Related papers

Existential contextuality and the models of Meyer, Kent, and Clifton

D. M. Appleby

It is shown that the models recently proposed by Meyer, Kent, and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.

arXiv:quant-ph/0005056•Physical Review A•Jan 10, 2002•27 citations

What does an experimental test of quantum contextuality prove or disprove?

Andreas Winter

The possibility of experimentally testing the Bell–Kochen–Specker theorem is investigated critically, following the demonstrations by Meyer, Kent, and Clifton–Kent that the predictions of quantum mechanics are indistinguishable (up to arbitrary precision) from those of a non-contextual model, and the subsequent debate about the extent to which these models are actually classical or non-contextual. The present analysis starts from a careful consideration of these 'finite-precision' approximations. A stronger condition for non-contextual models, dubbed ontological faithfulness , is exhibited. It is shown that this allows us to approximately formulate the constraints in Bell–Kochen–Specker theorems, such as to render the usual proofs robust. Consequently, one can experimentally test to finite precision ontologically faithful non-contextuality, and thus experimentally refute explanations from this smaller class. We include a discussion of the relation of ontological faithfulness to other proposals to overcome the finite precision objection. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

arXiv:1408.0945•Journal of Physics A Mathematical and Theoretical•Oct 9, 2014•42 citations

Comment on "Non-contextual hidden variables and physical measurements"

Adán Cabello

Kent's conclusion that ``non-contextual hidden variable theories cannot be excluded by theoretical arguments of the Kochen-Specker type once the imprecision in real world experiments is taken into account'' [Phys. Rev. Lett. 83, 3755 (1999)], is criticized. The Kochen-Specker theorem just points out that it is impossible even conceive a hidden variable model in which the outcomes of all measurements are pre-determined; it does not matter if these measurements are performed or not, or even if these measurements can be achieved only with finite precision.

arXiv:quant-ph/9911024•Nov 6, 1999•6 citations

Contextuality of Approximate Measurements

D. M. Appleby

The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement nullifies the Kochen-Specker theorem is criticised. It is argued that, although MKC have nullified the Kochen-Specker theorem strictly so-called, there are other, related propositions which are not nullified. The argument given is an elaboration of some of Mermin's critical remarks. Although MKC allow for the fact that the observables to be measured cannot be precisely specified, they continue to assume that the observables which are actually measured are strictly commuting. As Mermin points out, this assumption is unjustified. Consequently, the analysis of MKC is incomplete. To make it complete one needs to investigate the predictions their models make regarding approximate joint measurements of non-commuting observables. Such an investigation is carried out, using methods previously developed in connection with approximate joint measurements of position and momentum. It is shown that a form of contextuality then re-emerges.

arXiv:quant-ph/0005010•May 1, 2000•5 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

A hidden-variables versus quantum mechanics experiment

Adán Cabello, Guillermo García Alcaine

In the light of the Bell-Kochen-Specker theorem, we examine a feasible experimental test in order to discriminate between non-contextual hidden-variables and some probabilistic predictions of quantum mechanics.

Journal of Physics A Mathematical and General•Jul 7, 1995•12 citations
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen-Specker Theorem. Although we disagree with this last statement, the models play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality --with an emphasis on operational definitions-- and argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.
The possibility of experimentally testing the Bell–Kochen–Specker theorem is investigated critically, following the demonstrations by Meyer, Kent, and Clifton–Kent that the predictions of quantum mechanics are indistinguishable (up to arbitrary precision) from those of a non-contextual model, and the subsequent debate about the extent to which these models are actually classical or non-contextual. The present analysis starts from a careful consideration of these 'finite-precision' approximations. A stronger condition for non-contextual models, dubbed ontological faithfulness , is exhibited. It is shown that this allows us to approximately formulate the constraints in Bell–Kochen–Specker theorems, such as to render the usual proofs robust. Consequently, one can experimentally test to finite precision ontologically faithful non-contextuality, and thus experimentally refute explanations from this smaller class. We include a discussion of the relation of ontological faithfulness to other proposals to overcome the finite precision objection. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
Kent's conclusion that ``non-contextual hidden variable theories cannot be excluded by theoretical arguments of the Kochen-Specker type once the imprecision in real world experiments is taken into account'' [Phys. Rev. Lett. 83, 3755 (1999)], is criticized. The Kochen-Specker theorem just points out that it is impossible even conceive a hidden variable model in which the outcomes of all measurements are pre-determined; it does not matter if these measurements are performed or not, or even if these measurements can be achieved only with finite precision.
The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement nullifies the Kochen-Specker theorem is criticised. It is argued that, although MKC have nullified the Kochen-Specker theorem strictly so-called, there are other, related propositions which are not nullified. The argument given is an elaboration of some of Mermin's critical remarks. Although MKC allow for the fact that the observables to be measured cannot be precisely specified, they continue to assume that the observables which are actually measured are strictly commuting. As Mermin points out, this assumption is unjustified. Consequently, the analysis of MKC is incomplete. To make it complete one needs to investigate the predictions their models make regarding approximate joint measurements of non-commuting observables. Such an investigation is carried out, using methods previously developed in connection with approximate joint measurements of position and momentum. It is shown that a form of contextuality then re-emerges.
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.