Common causes for quantum identical particles

A. E. Allahverdyan; A. Hovhannisyan; S. Weigert

arxiv: 2606.21768 · v1 · pith:NZTSVSAFnew · submitted 2026-06-19 · 🪐 quant-ph · physics.data-an

Common causes for quantum identical particles

A. Hovhannisyan , S. Weigert , A. E. Allahverdyan This is my paper

Pith reviewed 2026-06-26 13:32 UTC · model grok-4.3

classification 🪐 quant-ph physics.data-an

keywords identical particlescommon causepermutation symmetryscreening variablesBell inequalitiescommutative measurementsquantum correlations

0 comments

The pith

For identical quantum particles, symmetric common causes for joint probabilities either do not exist or are trivial.

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

The paper starts from the fact that non-identical particles allow non-trivial common causes for joint probabilities under commutative measurements. It then imposes the additional requirement that both the particles and any common cause must be permutation-symmetric. Under this symmetry constraint, and across different ways of extracting joint probabilities from the same data, the authors show that either no such symmetric common cause is needed because the particles can be secretly distinguishable, or any symmetric screening variable that exists fails to account for all single-measurement correlations.

Core claim

Violations of Bell inequalities show that non-commutative measurements on non-identical particles lack a single common cause, while commutative measurements on the same particles do admit non-trivial common causes. When the particles are identical, so that density matrices and observables are necessarily permutation-symmetric, the demand that any common cause must itself be permutation-symmetric leads to one of two outcomes: either symmetric common causes need not exist, meaning the particles can be hiddenly distinguishable, or symmetric screening variables exist but are trivial and cannot explain all single-measurement correlations.

What carries the argument

Permutation-symmetric screening variable (common cause) required to reproduce joint probabilities of commutative measurements on identical particles.

If this is right

Particles can be hiddenly distinguishable.
Symmetric screening variables, when they exist, are trivial.
No single common cause can explain all single-measurement correlations.
The usual assumption that identical particles require symmetric common causes leads to these two alternatives.

Where Pith is reading between the lines

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

The result suggests that indistinguishability may not be fundamental but could mask underlying distinguishability in common-cause models.
It raises the question whether similar symmetry constraints on common causes appear in other symmetric quantum systems such as many-body states.
One could test the alternatives by checking whether relaxing permutation symmetry on the common cause recovers non-trivial explanations for observed correlations.

Load-bearing premise

It is natural to demand that the common cause describing joint probabilities is also permutation symmetric.

What would settle it

An explicit non-trivial permutation-symmetric common cause that reproduces all joint probabilities for a concrete pair of identical particles under commutative measurements, or a general proof that no such non-trivial cause can exist.

read the original abstract

Violations of Bell's inequalities imply that joint probabilities generated by non-commutative measurements on two (non-identical) quantum particles do not have a single common cause. But joint probabilities generated for such non-identical particles via commutative measurements do have non-trivial common cause variables. We focus on commutative measurements and consider two identical quantum particles, whose density matrices and observables (hermitian operators) are necessarily permutation-symmetric. It is natural to demand that the common cause describing joint probabilities is also permutation symmetric, i.e., it acts symmetrically on both particles. Looking at various ways of defining joint probabilities from the same measurement data, we conclude that either symmetric common causes need not exist (i.e., that the particles can be hiddenly distinguishable), or that symmetric screening variables exist, but they are trivial, i.e., no single common cause can explain all single-measurement correlations.

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.

Desk Editor's Note private letter to a colleague

The paper's disjunction on symmetric common causes for identical particles rests on an assumption that the hidden variable itself must respect permutation symmetry, which the quantum statistics do not force.

read the letter

The main takeaway is that for commutative measurements on identical particles the usual non-trivial common-cause story either fails if symmetry is imposed on the cause, or the causes become too weak to screen off all single-particle correlations. The authors extend the common-cause framework from distinguishable particles to the identical case by noting that density operators and observables are already permutation symmetric, then ask what that implies for joint probabilities defined in different ways.

What the paper does is flag a tension that had not been spelled out before: once particles are indistinguishable at the quantum level, demanding a symmetric screening variable leads to the stated choice between hidden distinguishability and triviality. That is a clean way to pose the question.

The soft spot is the step that treats symmetry of the cause as natural or required. The quantum description constrains only the observable statistics; an asymmetric hidden-variable model can still reproduce symmetric joints and marginals. The abstract gives no derivation showing why the internal labeling of the common cause must itself be symmetric, so the disjunction does not automatically follow. Without seeing the explicit constructions of the joint probabilities it is also hard to judge how robust the triviality claim is.

This is for readers already working on common-cause accounts of quantum correlations or on hidden-variable models for identical particles. It is not a major shift but it sharpens an existing issue. The work shows clear engagement with the literature and is worth sending to referees even if the central premise needs more defense.

Referee Report

1 major / 0 minor

Summary. The manuscript argues that violations of Bell inequalities show non-commutative joint probabilities on non-identical particles lack a single common cause, while commutative measurements admit non-trivial common causes. For identical particles the density operator and observables are necessarily permutation-symmetric; the authors treat it as natural to require the same symmetry of any common-cause variable. Examining different ways of defining joint probabilities from the same data, they conclude that either no symmetric common cause exists (particles are hiddenly distinguishable) or any such cause is trivial and cannot screen off all single-particle correlations.

Significance. If the central disjunction is established, the result would constrain common-cause models for indistinguishable particles and sharpen the distinction between identical and non-identical cases in quantum foundations. The paper correctly notes that commutative measurements on non-identical particles do admit common causes, providing a useful contrast. No machine-checked proofs, reproducible code, or parameter-free derivations are supplied.

major comments (1)

[Abstract] Abstract: the central disjunction rests on the premise that 'it is natural to demand that the common cause describing joint probabilities is also permutation symmetric.' No derivation is given showing why an asymmetric hidden-variable model is forbidden once the observable statistics are required only to be symmetric; the symmetry of the density operator and observables constrains the marginals and joints but does not by itself force the internal labeling of the screening variable to be symmetric. This assumption is load-bearing for both arms of the claimed dichotomy.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting the need to strengthen the justification of our central assumption. We address the major comment below and agree that the manuscript will benefit from an explicit derivation of the symmetry requirement.

read point-by-point responses

Referee: [Abstract] Abstract: the central disjunction rests on the premise that 'it is natural to demand that the common cause describing joint probabilities is also permutation symmetric.' No derivation is given showing why an asymmetric hidden-variable model is forbidden once the observable statistics are required only to be symmetric; the symmetry of the density operator and observables constrains the marginals and joints but does not by itself force the internal labeling of the screening variable to be symmetric. This assumption is load-bearing for both arms of the claimed dichotomy.

Authors: We agree that the manuscript would be improved by an explicit justification for requiring the common cause to be permutation-symmetric. The rationale, which we will now spell out, is that indistinguishability is a fundamental symmetry of the physical description: any model that assigns the particles an internal label via an asymmetric hidden variable would effectively render them distinguishable, contradicting the premise that the particles are identical. This is directly analogous to the requirement that both the density operator and the observables themselves be symmetric under exchange. An asymmetric screening variable would therefore introduce a distinction that is absent from the observable statistics and from the Hilbert-space description. In the revised version we will add a concise paragraph (likely in Section 2) deriving this requirement from the principle that the entire common-cause model must respect the same exchange symmetry as the quantum state and measurement operators. revision: yes

Circularity Check

0 steps flagged

No circularity: conceptual premise on symmetry is stated explicitly as an assumption, not derived from or reduced to the conclusion

full rationale

The paper's central move is an explicit normative premise ('It is natural to demand that the common cause ... is also permutation symmetric') followed by an examination of joint-probability constructions under that premise. No equations, parameter fits, or self-citations appear in the supplied text that would make the disjunction (no symmetric common cause or trivial common cause) equivalent to the input by construction. The symmetry requirement is presented as an additional demand rather than a theorem derived from the quantum description itself, so the argument does not collapse into self-definition or fitted-input renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no free parameters, axioms, or invented entities are described.

pith-pipeline@v0.9.1-grok · 5680 in / 872 out tokens · 13412 ms · 2026-06-26T13:32:48.422644+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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[1] [1]

Reichenbach,The direction of time

H. Reichenbach,The direction of time. University of California Press, 1956, vol. 65

1956

[2] [2]

Suppes,A probabilistic theory of causality

P. Suppes,A probabilistic theory of causality. North- Holland, Amsterdam, 1970

1970

[3] [3]

The principle of the common cause faces the bernstein paradox,

J. Uffink, “The principle of the common cause faces the bernstein paradox,”Philosophy of Science, vol. 66, no. S3, pp. S512–S525, 1999

1999

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Hofer-Szab´ o, M

G. Hofer-Szab´ o, M. R´ edei, and L. E. Szab´ o,The principle of the common cause. Cambridge University Press, 2013

2013

[5] [5]

Correlations genuine and spurious in pearson and yule,

J. Aldrich, “Correlations genuine and spurious in pearson and yule,”Statistical science, pp. 364–376, 1995

1995

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J. Pearl,Causality. Cambridge university press, 2009

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J. Peters, D. Janzing, and B. Sch¨ olkopf,Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017

2017

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O. Penrose and I. C. Percival, “The direction of time,” Proceedings of the Physical Society, vol. 79, no. 3, p. 605, 1962

1962

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A causal-model theory of conceptual repre- sentation and categorization

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2003

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Common cause explanation,

E. Sober, “Common cause explanation,”Philosophy of Science, vol. 51, no. 2, pp. 212–241, 1984

1984

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A. Hovhannisyan and A. Allahverdyan, “Resolution of simpson’s paradox via the common cause principle,” in Proceedings of the 39th Conference on Neural Information Processing Systems (NeurIPS 2025), San Diego, USA, 2025

2025

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2018

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1971

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Contextuality and indistinguishability,

J. A. De Barros, F. Holik, and D. Krause, “Contextuality and indistinguishability,”Entropy, vol. 19, no. 9, p. 435, 2017

2017

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J. A. de Barros, F. Holik, and D. Krause, “Indistinguisha- bility and the origins of contextuality in physics,”Philo- sophical Transactions of the Royal Society A, vol. 377, no. 2157, p. 20190150, 2019

2019

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Dynamical symmetrization of the state of iden- tical particles,

A. E. Allahverdyan, K. V. Hovhannisyan, and D. Pet- rosyan, “Dynamical symmetrization of the state of iden- tical particles,”Proceedings of the Royal Society A, vol. 477, no. 2249, p. 20200911, 2021

2021

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Nonnegative ranks, decompositions, and factorizations of nonnegative matri- ces,

J. E. Cohen and U. G. Rothblum, “Nonnegative ranks, decompositions, and factorizations of nonnegative matri- ces,”Linear Algebra and its Applications, vol. 190, pp. 149–168, 1993

1993

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The most likely common cause,

A. Hovhannisyan and A. E. Allahverdyan, “The most likely common cause,”International Journal of Approxi- mate Reasoning, vol. 173, p. 109264, 2024

2024

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Re- ichenbachian common cause clusters,

C. Mazzola, D. Kinkead, P. Ellerton, and D. Brown, “Re- ichenbachian common cause clusters,”Erkenntnis, pp. 1– 29, 2020

2020

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Reichenbachian common cause systems re- visited,

C. Mazzola, “Reichenbachian common cause systems re- visited,”Foundations of Physics, vol. 42, pp. 512–523, 2012

2012

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Nonnegative matrix factorization and the principle of the common cause,

E. Khalafyan, A. E. Allahverdyan, and A. Hovhannisyan, “Nonnegative matrix factorization and the principle of the common cause,” inProceedings of the IEEE Inter- national Conference on Data Science and Advanced Ana- lytics (DSAA 2025), 2025

2025

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Quantum states with einstein-podolsky- rosen correlations admitting a hidden-variable model,

R. F. Werner, “Quantum states with einstein-podolsky- rosen correlations admitting a hidden-variable model,” Physical Review A, vol. 40, no. 8, p. 4277, 1989

1989

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Interference of non- identical particles’,

V. Lyuboshitz and M. Podgoretskii, “Interference of non- identical particles’,”Soviet Physics JETP, vol. 28, pp. 469–75, 1969

1969

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From single-particle states to n-particle states,

Y. Tikochinsky, “From single-particle states to n-particle states,”Physical Review A, vol. 37, no. 9, p. 3553, 1988

1988

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Simple proof of the sym- metrization postulate in quantum mechanics,

Y. Tikochinsky and D. Shalitin, “Simple proof of the sym- metrization postulate in quantum mechanics,”American Journal of Physics, vol. 58, no. 1, pp. 78–79, 1990

1990

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Informational approach to the quantum sym- metrization postulate,

P. Goyal, “Informational approach to the quantum sym- metrization postulate,”New Journal of Physics, vol. 17, no. 1, p. 013043, 2015

2015

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Nonnegative factorization of positive semidefinite nonnegative matrices,

L. J. Gray and D. G. Wilson, “Nonnegative factorization of positive semidefinite nonnegative matrices,”Linear al- gebra and its applications, vol. 31, pp. 119–127, 1980

1980

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Some simple remarks about quantum nonseparability for systems composed of identical constituents,

G. C. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,”Il Nuovo Ci- mento B (1971-1996), vol. 39, no. 1, pp. 130–134, 1977

1971

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Bell’s theorem and the different concepts of locality,

P. H. Eberhard, “Bell’s theorem and the different concepts of locality,”Il Nuovo Cimento B (1971-1996), vol. 46, no. 2, pp. 392–419, 1978

1971

[39] [39]

The lesson of causal dis- covery algorithms for quantum correlations: causal expla- nations of bell-inequality violations require fine-tuning,

C. J. Wood and R. W. Spekkens, “The lesson of causal dis- covery algorithms for quantum correlations: causal expla- nations of bell-inequality violations require fine-tuning,” New Journal of Physics, vol. 17, no. 3, p. 033002, 2015. Appendix: Common cause, quantum entangle- ment and Bell inequalities. –The assumptions that go into derivations of Bell’s in...

2015

[40] [40]

(43) is analogous to (32, 34) and allows to derive the Bell-CHSH inequality (36)

lead from (40): p(u, v|Ak, Bl) = X c p(c)p(u|Ak, c)p(v|Bl, c).(43) Eq. (43) is analogous to (32, 34) and allows to derive the Bell-CHSH inequality (36). p-7