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arxiv: 2605.24446 · v2 · pith:I4V3PHXMnew · submitted 2026-05-23 · 🪐 quant-ph

Distinguishing Bohmian contextuality from Kochen-Specker contextuality

Anton Skott , Jan-{\AA}ke Larsson This is my paper

Pith reviewed 2026-06-30 13:34 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum contextualityKochen-Specker theoremBohmian mechanicshidden-variable modelsontological modelscontextual ontological model
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The pith

A hidden-variable model can produce Kochen-Specker contextuality while determining every measurement outcome from the ontic state alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that Bohmian contextuality, in which some outcomes depend on apparatus details beyond the model state, is not required to obtain Kochen-Specker contextuality in a hidden-variable theory. The Contextual Ontological Model achieves the KS predictions while ensuring every allowed measurement outcome is fixed by the ontic state. This separation shows the two notions of contextuality are logically independent. A sympathetic reader would care because it removes an assumed link between distinct flavours of contextuality and opens the possibility of studying them in isolation.

Core claim

The recently proposed Contextual Ontological Model produces KS contextual predictions but does not have the Bohmian contextuality; the outcome of every measurement allowed by COM can be predicted from the model state itself. This distinguishes Bohmian contextuality from KS contextuality, and enables individual study of the two concepts.

What carries the argument

The Contextual Ontological Model (COM), a hidden-variable theory that reproduces quantum KS-contextual predictions while keeping all measurement outcomes fully determined by the ontic state.

If this is right

  • KS contextuality can appear in ontological models that lack any device-dependent outcome assignment.
  • The two contextuality notions can be investigated independently in the same framework.
  • COM supplies a concrete counter-example to any claim that Bohmian-style contextuality is necessary for KS contextuality.
  • All measurements permitted by COM remain deterministic functions of the ontic state.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar constructions might separate other pairs of contextuality or nonlocality notions that are currently conflated.
  • Experimental tests could focus on KS inequalities while enforcing strict device independence to isolate the KS component.
  • The existence of such models suggests that proofs requiring Bohmian contextuality to obtain KS contextuality rest on an extra assumption not forced by quantum theory itself.

Load-bearing premise

That the COM is a valid hidden-variable model that exactly reproduces the quantum predictions required for KS contextuality while fixing every outcome by the ontic state.

What would settle it

An explicit calculation or simulation showing that some measurement allowed by the COM rules yields an outcome not fixed by the ontic state, or that the COM fails to reproduce a KS-contextual correlation in a concrete finite-dimensional system.

Figures

Figures reproduced from arXiv: 2605.24446 by Anton Skott, Jan-{\AA}ke Larsson.

Figure 2
Figure 2. Figure 2: FIG. 2. One possible Bohmian trajectory among others for a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Spin system behavior at SG device, with spatial wave [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. One possible Bohmian trajectory among others for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Quantum contextuality is a concept used to describe the property of hidden-variable theory that measurement outcomes predetermined by the hidden variables depend on the measurement context. The term measurement context can have different meanings, giving rise to different flavours of quantum contextuality. The first discovered flavour is Kochen-Specker (KS) contextuality where measurement outcomes will depend on what compatible measurements are jointly performed with the selected measurement. Another flavour, here to be compared with KS contextuality, is that referred to in Bohmian mechanics where outcomes of some specific measurements are not completely specified by the model state, but depend also on specifics of the measurement device used. It has been claimed that this type of Bohmian contextuality is necessary to enable KS contextuality in a hidden variable model. In this paper we show that this is not the case. The recently proposed Contextual Ontological Model (COM) [Hindlycke and Larsson, Phys. Rev. Lett. 2022] produces KS contextual predictions but does not have the Bohmian contextuality; the outcome of every measurement allowed by COM can be predicted from the model state itself. This distinguishes Bohmian contextuality from KS contextuality, and enables individual study of the two concepts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper claims that Kochen-Specker (KS) contextuality and Bohmian contextuality are distinct notions in hidden-variable theories. It shows that the Contextual Ontological Model (COM) from Hindlycke and Larsson (PRL 2022) reproduces KS-contextual quantum statistics while remaining fully deterministic: every allowed measurement outcome is fixed by the ontic state alone, with no additional dependence on measurement-device specifics. This is presented as a counterexample to the claim that Bohmian contextuality is required to enable KS contextuality, thereby allowing the two concepts to be studied independently.

Significance. If the central claim holds, the result supplies a concrete, deterministic ontological model that separates KS contextuality from Bohmian contextuality. This strengthens the conceptual toolkit for analyzing contextuality by showing that device-dependent outcome assignment is not a necessary ingredient for reproducing KS-contextual marginals. The paper thereby opens the possibility of examining each notion on its own terms without conflating them.

minor comments (2)
  1. [Abstract / §1] The abstract and introduction would benefit from a one-sentence reminder of the precise definition of Bohmian contextuality used in the COM construction (e.g., explicit reference to the relevant equation or section in the 2022 PRL).
  2. [§2] A brief table or diagram contrasting the two contextuality notions (KS vs. Bohmian) with respect to outcome determination would improve readability for readers unfamiliar with the COM framework.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation to accept. The referee's summary correctly identifies the central result: that the Contextual Ontological Model provides a deterministic hidden-variable theory reproducing KS-contextual statistics without Bohmian contextuality.

Circularity Check

0 steps flagged

Minor self-citation to prior COM definition; distinction remains independent

full rationale

The paper's argument relies on the COM model from Hindlycke and Larsson (PRL 2022), whose authors overlap. This citation introduces the model whose properties (KS contextuality with outcomes fixed by ontic state alone) are then used to separate the two notions of contextuality. No derivation step in the present paper reduces a prediction or uniqueness claim to a fitted parameter or self-referential definition; the separation follows directly from the stated model properties without internal circular reduction. This qualifies as one minor self-citation that is not load-bearing for the central distinction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.1-grok · 5750 in / 841 out tokens · 30849 ms · 2026-06-30T13:34:00.560066+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

17 extracted references · 2 canonical work pages · 2 internal anchors

  1. [1]

    Kochen and E

    S. Kochen and E. P. Specker, Journal of Mathematics and Mechanics17, 59 (1967)

    1967

  2. [2]

    Budroni, A

    C. Budroni, A. Cabello, O. G¨ uhne, M. Kleinmann, and J.-˚A. Larsson, Reviews of Modern Physics94, 045007 (2022)

    2022

  3. [3]

    D. Z. Albert,Quantum Mechanics and Experience(Har- vard University Press, Cambridge MA, 1992)

    1992

  4. [4]

    Hardy, inBohmian Mechanics and Quantum Theory: An Appraisal, Boston Studies in the Philosophy of Sci- ence, Vol

    L. Hardy, inBohmian Mechanics and Quantum Theory: An Appraisal, Boston Studies in the Philosophy of Sci- ence, Vol. 184, edited by J. T. Cushing, A. Fine, and S. Goldstein (Springer, Dordrecht, 1996) pp. 67–76

    1996

  5. [5]

    Norsen, American Journal of Physics82, 337 (2014)

    T. Norsen, American Journal of Physics82, 337 (2014). 7

    2014

  6. [6]

    Bohm, Physical Review85, 166 (1952)

    D. Bohm, Physical Review85, 166 (1952)

    1952

  7. [7]

    P. R. Holland,The Quantum Theory of Motion: An Ac- count of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics(Cambridge University Press, Cam- bridge, 1993)

    1993

  8. [8]

    Hindlycke and J.- ˚A

    C. Hindlycke and J.- ˚A. Larsson, Physical Review Letters 129, 130401 (2022)

    2022

  9. [9]

    The Contextual Heisenberg Microscope

    J.- ˚A. Larsson, Physical Review A113, 042215 (2026), arXiv:2504.20816

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  10. [10]

    The Heisenberg Representation of Quantum Computers

    D. Gottesman, The Heisenberg Representation of Quan- tum Computers (1998), arXiv:quant-ph/9807006

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  11. [11]

    Aaronson and D

    S. Aaronson and D. Gottesman, Physical Review A70, 052328 (2004)

    2004

  12. [12]

    Naaman-Marom, N

    G. Naaman-Marom, N. Erez, and L. Vaidman, Annals of Physics327, 2522 (2012)

    2012

  13. [13]

    D¨ urr, S

    D. D¨ urr, S. Goldstein, and N. Zangh` ı,Quantum Physics Without Quantum Philosophy(Springer, Berlin, Heidel- berg, 2013)

    2013

  14. [14]

    D¨ urr, S

    D. D¨ urr, S. Goldstein, and N. Zangh´ ı, Journal of Statis- tical Physics67, 843 (1992)

    1992

  15. [15]

    R. E. Wyatt,Quantum Dynamics with Trajectories, In- terdisciplinary Applied Mathematics, Vol. 28 (Springer- Verlag, New York, 2005)

    2005

  16. [16]

    Teufel and D

    S. Teufel and D. D¨ urr,Bohmian Mechanics: The Physics and Mathematics of Quantum Theory(Springer, Berlin, Heidelberg, 2009)

    2009

  17. [17]

    J. S. Bell, Physics Physique Fizika1, 195 (1964)

    1964