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A multipartite quantum system can lack any single classical hidden-variable model even when every local subsystem and every measured context separately admits one.

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2026-06-29 12:06 UTC pith:DEUJ5XFP

load-bearing objection This paper gives three explicit bipartite constructions that separate global contextuality from both local noncontextuality and per-context generalized Bell nonlocality within a no-cross-party-joint-measurement framework.

arxiv 2605.28702 v2 pith:DEUJ5XFP submitted 2026-05-27 quant-ph

Global Kochen-Specker Contextuality Without Local Contextuality and Generalized Bell Nonlocality

Ming Yang This is my paper
classification quant-ph
keywords global contextualityKochen-Specker theoremBell nonlocalityhidden variable modelsmultipartite systemscompositionalityKCBS scenario
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes that in a general Bell-type framework with multiple parties and local compatible contexts but no cross-party joint measurements, the lack of local contextuality together with the existence of generalized local hidden-variable descriptions for each multipartite context does not guarantee a single noncontextual hidden-variable model for the whole system. This separation is shown by three explicit bipartite constructions, one giving a direct obstruction, one algebraic at the scenario level, and one at the state level using a flagged Werner state. A sympathetic reader would care because it demonstrates that classical explanations fail to compose across parties even when all local and per-context tests pass, revealing contextuality as a genuinely compositional feature of quantum data.

Core claim

Within the general Bell-type framework considered here, with arbitrary parties and arbitrary local compatible contexts, but no cross-party joint measurements, the absence of local contextuality and GLHV-type generalized Bell nonlocality does not imply the existence of a global noncontextual hidden-variable model. Three bipartite constructions exhibit this separation: a polarization-path construction gives a direct global obstruction, a qubit-qutrit KCBS construction gives an algebraic scenario-level example with explicit formulas for the unconditional KCBS operator and correlation-polytope constraints, and a flagged qutrit Werner-local state gives a state-level example where the state is ent

What carries the argument

Global contextuality, the obstruction to promoting per-context generalized local hidden-variable descriptions into one noncontextual hidden-variable model for the entire multipartite system.

Load-bearing premise

The three explicit bipartite constructions each satisfy local noncontextuality plus per-context GLHV descriptions while exhibiting a global obstruction to any single noncontextual hidden-variable model.

What would settle it

Explicitly constructing one noncontextual hidden-variable model that simultaneously reproduces the local marginals, the per-context statistics, and the postselected global correlations in the polarization-path or flagged qutrit Werner construction would falsify the separation.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The classical composition lemma, which absorbs conditional hidden variables into a single larger variable, fails to hold for the quantum data in these constructions.
  • Local noncontextuality and per-context GLHV descriptions are insufficient to guarantee global noncontextuality in multipartite systems without cross-party measurements.
  • Global contextuality constitutes a compositional obstruction to classical explanation separate from ordinary local Bell or Kochen-Specker violations.
  • The separation can appear both at the level of measurement scenarios and at the level of specific quantum states.

Where Pith is reading between the lines

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

  • In quantum networks or distributed sensing, contextuality certificates may need to be evaluated globally rather than assembled from local checks.
  • The constructions suggest that adding cross-party joint measurements could restore or break the possibility of a single classical model in ways the current framework excludes.
  • One could test whether the separation persists or strengthens when the number of parties is increased beyond two while keeping the same local noncontextuality conditions.
  • The result isolates contextuality as a property that can be detected only after the full composition of the system is considered.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The paper claims that, within a general Bell-type framework allowing arbitrary parties and local compatible contexts but forbidding cross-party joint measurements, the absence of local contextuality and of GLHV-type generalized Bell nonlocality does not entail the existence of a single global noncontextual hidden-variable model. This separation is witnessed by three explicit bipartite constructions (polarization-path, qubit-qutrit KCBS scenario, and flagged qutrit Werner-local state) together with a classical composition lemma showing that classical conditional hidden variables can be absorbed into a larger hidden variable while quantum contextual data need not factorize in the same way.

Significance. If the constructions hold, the result isolates a genuinely compositional form of contextuality that is invisible to all local tests and to per-context GLHV descriptions. The manuscript supplies explicit operator expressions, correlation-polytope constraints, and postselection rules for the KCBS example, which constitute verifiable, parameter-free witnesses rather than fitted or self-referential arguments. This strengthens the conceptual distinction between local and global nonclassicality and supplies concrete counter-examples to the expectation that local noncontextuality plus per-context classicality should promote to a global NCHV model.

minor comments (3)
  1. §3.2, after Eq. (17): the postselection rule for the flagged Werner state is stated only in words; an explicit projector or indicator function would make the global obstruction calculation fully reproducible from the given operators.
  2. Figure 2 caption: the labeling of the three contexts in the polarization-path construction is not aligned with the operator list in the preceding paragraph; a one-line cross-reference would remove ambiguity.
  3. §4, paragraph 3: the classical composition lemma is proved for deterministic hidden variables; a short remark on whether the argument extends to stochastic local models would clarify the scope.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our work, which correctly identifies the separation between global contextuality and the absence of local contextuality or GLHV nonlocality in the bipartite constructions. The recommendation for minor revision is noted. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via explicit constructions

full rationale

The paper's central claim is witnessed by three explicit bipartite constructions (polarization-path, qubit-qutrit KCBS, flagged qutrit Werner-local state) together with a classical composition lemma that is spelled out inside the manuscript. Each construction supplies concrete operator expressions, polytope constraints, and postselection rules that are directly calculable, so the separation between local noncontextuality/GLHV descriptions and the absence of a global NCHV model is established by direct verification rather than by any self-definitional reduction, fitted-parameter renaming, or load-bearing self-citation. No step in the provided text reduces a claimed prediction or uniqueness result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper operates within standard quantum mechanics and the established definitions of contextuality and hidden-variable models; no additional free parameters, ad-hoc axioms, or invented entities are introduced beyond the new terminology of global contextuality.

axioms (1)
  • standard math Standard axioms of quantum mechanics and the definitions of noncontextual hidden-variable models
    The constructions rely on the usual Hilbert space formalism and the standard notion of noncontextuality.

pith-pipeline@v0.9.1-grok · 5808 in / 1213 out tokens · 37118 ms · 2026-06-29T12:06:51.763810+00:00 · methodology

0 comments
read the original abstract

A set of quantum data can look classical in every local test and still fail to admit a single classical explanation of the whole composite system. We formulate this failure as global contextuality. Here global means global in the physical sense of the whole multipartite system, not the local/global terminology of sheaf theory. Each party's local statistics are noncontextual and each measured multipartite context admits a generalized local hidden-variable description, but the GLHV block descriptions cannot be promoted to a single noncontextual hidden-variable model for the whole system. Three bipartite constructions exhibit this separation. A polarization-path construction gives a direct global obstruction. A qubit-qutrit KCBS construction gives an algebraic scenario-level example, with explicit formulas for the unconditional KCBS operator, the correlation-polytope constraints, and the postselected violation. A flagged qutrit Werner-local state gives a state-level example: the state is entangled and local for all projective measurements, its local qutrit marginals do not violate KCBS, yet postselection rules out a single GNCHV model. We also spell out the classical composition lemma: classical conditional hidden variables can be absorbed into a larger hidden variable, whereas quantum contextual data need not allow such a factorization. Within the general Bell-type framework considered here, with arbitrary parties and arbitrary local compatible contexts, but no cross-party joint measurements, the absence of local contextuality and GLHV-type generalized Bell nonlocality does not imply the existence of a global noncontextual hidden-variable model. Global contextuality is thus a compositional obstruction to classical explanation.

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Genuine Global Kochen-Specker Contextuality as Classical Coordination Cost

    quant-ph 2026-06 unverdicted novelty 7.0

    Genuine global KS contextuality is framed as the classical coordination cost needed to maintain a global noncontextual explanation from locally available information in multipartite systems.

Reference graph

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