arxiv: 2605.03120 · v1 · submitted 2026-05-04 · 🪐 quant-ph

Coordination Requires a Common Cause in Quantum Theory

Daniel Centeno , Antoine Coquet , Maria Ciudad Ala\~n\'on , Lucas Tendick , Marc-Olivier Renou , Elie Wolfe This is my paper

Pith reviewed 2026-05-08 18:31 UTC · model grok-4.3

classification 🪐 quant-ph

keywords coordination principlecommon causequantum theoryBell inequalitiesGHZ stateno-signalingmultipartite coordination

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The pith

In quantum theory, four parties can achieve perfect randomized coordination only if they share a common cause.

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

The paper introduces the coordination principle as a multipartite extension of Reichenbach's common cause principle, under which parties achieve perfect randomized coordination—agreeing on a uniformly random output—only if they all share a common cause. It demonstrates that this principle does not follow from standard no-signaling and statistical independence by constructing an explicit counterexample theory that satisfies those but violates coordination. In quantum theory, however, the principle holds for four parties, with noise-tolerant Bell-like inequalities derived to certify the presence of a common cause. These results are extended to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause certifiable by experimentally accessible inequalities.

Core claim

We propose the coordination principle: parties in a network can achieve perfect randomized coordination only if they all share a common cause. This principle does not follow from no-signaling and independence, as shown by an explicit theory that satisfies those conditions yet violates coordination. The principle holds in quantum theory for four parties, where noise-tolerant Bell-like inequalities certify a common cause. For the genuinely quantum coordination task with the four-partite GHZ state, a quantum common cause is required and can also be certified by experimentally accessible Bell-like inequalities.

What carries the argument

The coordination principle, which asserts that perfect randomized coordination among parties is possible only given a shared common cause, together with the derived noise-tolerant Bell-like inequalities that certify such a cause in quantum settings.

If this is right

The coordination principle holds in quantum theory for four parties.
Noise-tolerant Bell-like inequalities certify a common cause for coordination tasks.
The four-partite GHZ state requires a quantum common cause.
A quantum common cause for the GHZ coordination task can be certified by experimentally accessible Bell-like inequalities.
The coordination principle is satisfied in quantum theory for general N parties.

Where Pith is reading between the lines

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

This separation between quantum theory and other no-signaling theories may enable new experimental tests for the presence of common causes in multipartite quantum networks.
The framework could be applied to certify common causes in other quantum information tasks involving agreement or correlation.
Relaxing the perfect-coordination requirement to approximate versions might yield practical certification protocols for near-term devices.
The results suggest that quantum causal structures impose stricter constraints on multipartite coordination than classical or general no-signaling models.

Load-bearing premise

The definition of perfect randomized coordination as producing a uniformly random output with probability exactly one, combined with the assumptions that the underlying theory obeys no-signaling and statistical independence.

What would settle it

An explicit four-party quantum strategy that achieves perfect randomized coordination while violating one of the derived noise-tolerant Bell-like inequalities, or an experimental observation of such coordination without a detectable common cause.

Figures

Figures reproduced from arXiv: 2605.03120 by Antoine Coquet, Daniel Centeno, Elie Wolfe, Lucas Tendick, Marc-Olivier Renou, Maria Ciudad Ala\~n\'on.

**Figure 1.** Figure 1: FIG. 1 view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

read the original abstract

We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.

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 manuscript proposes the coordination principle, a multipartite extension of Reichenbach's common cause principle, according to which parties achieve perfect randomized coordination (agreeing on a uniformly random output with probability 1) only if they share a common cause. It constructs an explicit no-signaling theory that satisfies no-signaling and statistical independence yet violates the coordination principle, showing the principle is independent of those assumptions. The authors prove that the coordination principle holds in quantum theory for four parties, derive noise-tolerant Bell-like inequalities that certify a common cause, and extend the results to a genuinely quantum coordination task with the four-partite GHZ state, which requires a quantum common cause also certifiable by experimentally accessible Bell-like inequalities. A companion paper generalizes the results to N parties.

Significance. If the derivations hold, this work establishes a new causal principle that is satisfied specifically in quantum theory (but not in general no-signaling theories), along with experimentally testable inequalities for certifying common causes in multipartite settings. Strengths include the explicit counterexample theory violating the principle while obeying standard assumptions, the direct proofs inside quantum theory, and the application to the GHZ state with falsifiable predictions. These elements provide a clear separation from general theories and practical certification tools.

minor comments (2)

The definition of 'perfect randomized coordination' (uniform random output with probability 1) is central to the principle and the separation from general theories; state it explicitly with the associated probability measure in the main text before the counterexample construction.
In the derivation of the noise-tolerant Bell-like inequalities for four parties, include a brief remark on how the inequalities behave under the bipartite limit or when one party is traced out, to clarify the genuinely multipartite character.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, the clear summary of its contributions, and the recommendation for minor revision. We appreciate the recognition of the work's significance in establishing a new causal principle specific to quantum theory along with experimentally testable inequalities.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper defines the coordination principle as a multipartite extension of Reichenbach's common cause, exhibits an explicit no-signaling theory that satisfies standard assumptions yet violates the principle, and then supplies a direct mathematical proof that the principle holds inside quantum theory for four parties together with the associated noise-tolerant Bell inequalities. These steps rely on the axioms of quantum mechanics and the stated no-signaling plus independence conditions without any reduction to fitted parameters, self-referential definitions, or load-bearing self-citations; the companion paper is invoked solely for the N-party generalization and plays no role in establishing the four-party result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces the coordination principle itself as a new causal axiom that does not follow from no-signaling and independence. No free parameters or invented physical entities are mentioned in the abstract; the common cause is treated as an existing concept being applied to a new task.

axioms (1)

domain assumption No-signaling and statistical independence principles
The abstract states that the coordination principle does not follow from these standard principles, which are therefore presupposed as background.

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discussion (0)

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Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Cost.Jcost / Foundation.LogicAsFunctionalEquation washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

⟨AB⟩+⟨BC⟩+⟨CD⟩ ≤ ⟨A⟩⟨D⟩/2 + 3√3/2

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

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