arxiv: 2510.12886 · v2 · submitted 2025-10-14 · 🪐 quant-ph

Can outcome communication explain Bell nonlocality?

Carlos Vieira , Carlos de Gois , Pedro Lauand , Lucas E. A. Porto , S\'ebastien Designolle , Marco T\'ulio Quintino This is my paper

Pith reviewed 2026-05-18 07:15 UTC · model grok-4.3

classification 🪐 quant-ph

keywords Bell nonlocalityoutcome communicationlocal hidden variable modelsqubit-qudit entanglementprojective measurementsquantum correlationsclassical simulation

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The pith

For any qubit-qudit state, an LHV model with outcome communication exists if and only if one without communication does when all projective measurements are considered.

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

The paper proves that allowing communication of measurement outcomes between observers cannot account for the Bell nonlocality of entangled qubit-qudit states if the model has to match the statistics of every projective measurement. In this full-measurement scenario, the presence of outcome communication provides no extra explanatory power beyond standard local hidden variable models. This contrasts with cases where only a limited set of measurements is required, where outcome communication can indeed help reproduce some nonlocal correlations. The result shows that the requirement to cover all projective measurements makes outcome communication ineffective for explaining nonlocality in these systems.

Core claim

A qubit-qudit system under projective measurements admits an LHV model with outcome communication if and only if it admits an LHV model without communication. This equivalence demonstrates that outcome communication does not suffice to explain the quantum correlations arising from any entangled qubit-qudit state when all projective measurements must be reproduced.

What carries the argument

The outcome-communication augmented LHV model, which allows parties to exchange their measurement outcomes to potentially simulate quantum correlations, shown to be equivalent to the standard LHV model for full projective measurements on qubit-qudit systems.

If this is right

Quantum correlations from qubit-qudit entanglement that violate Bell inequalities cannot be explained by LHV models even with outcome communication, for the complete set of projective measurements.
Restricted measurement sets, such as qubit measurements restricted to the upper hemisphere of the Bloch ball, allow outcome communication to provide an advantage over standard LHV models.
Properties like deterministic measurements and the ability to relabel outcomes become crucial when communication of outcomes is permitted.
Trivial aspects in standard Bell scenarios gain importance in the presence of outcome communication.

Where Pith is reading between the lines

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

If outcome communication of this limited type cannot explain nonlocality, then broader forms of classical communication might be necessary to classically simulate quantum correlations.
The result may extend to suggest that for higher-dimensional systems or different measurement types, similar equivalences hold.

Load-bearing premise

That the model must exactly reproduce the correlations for every projective measurement on the qubit-qudit system, as opposed to only some selected measurements.

What would settle it

Finding a specific qubit-qudit entangled state where the quantum correlations for all projective measurements can be reproduced by an LHV model that uses outcome communication but cannot be reproduced by any LHV model without communication would falsify the main result.

Figures

Figures reproduced from arXiv: 2510.12886 by Carlos de Gois, Carlos Vieira, Lucas E. A. Porto, Marco T\'ulio Quintino, Pedro Lauand, S\'ebastien Designolle.

**Figure 1.** Figure 1: Different causal structures for bipartite Bell scenarios. (a) Standard Bell scenario, where the parties are correlated [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Pictorial representation of the relations between [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.

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

Outcome communication explains no more than a standard LHV model for qubit-qudit states under all projective measurements.

read the letter

The main thing to know is that this paper proves an equivalence: for any qubit-qudit state, you can have a local hidden variable model with outcome communication that reproduces all projective measurement correlations if and only if you already have one without communication. So outcome communication doesn't buy you anything extra in this setting. What stands out as new is the extension to the complete set of projective measurements. Earlier results apparently worked only when the number of inputs was finite, but here they handle the full continuous case for projective measurements on these systems. The paper handles this cleanly by contrasting it with restricted measurement sets. For example, when the qubit measurements are limited to the upper hemisphere of the Bloch ball, outcome communication does allow more correlations to be explained. This shows that the universal requirement is what kills the advantage. I think the argument is on solid ground. It rests on standard definitions of LHV models and the need to reproduce every projective measurement, without introducing extra assumptions that might weaken it. The note about deterministic outcomes and relabeling becoming non-trivial with communication is a useful observation. One minor point is that the result is specific to qubit-qudit states and projective measurements, so it doesn't immediately generalize to arbitrary dimensions or POVMs, but the paper doesn't claim otherwise. This is the kind of paper that foundations researchers will want to see. It sharpens the conditions under which communication helps or doesn't in simulating quantum correlations. A reader focused on classical models for entangled states would get direct value from the equivalence result. I would recommend putting this through peer review. The core claim looks worth checking in detail.

Referee Report

0 major / 2 minor

Summary. The manuscript proves that for any qubit-qudit state, an LHV model with outcome communication reproduces the correlations of all projective measurements if and only if a standard LHV model without communication does. This equivalence is contrasted with restricted measurement sets (e.g., qubit measurements restricted to the upper hemisphere of the Bloch ball), where outcome communication provides an advantage. The paper emphasizes that deterministic outcomes and outcome relabeling become nontrivial once communication is permitted.

Significance. If the central equivalence holds, the result sharply delineates when outcome communication can or cannot explain Bell nonlocality for qubit-qudit systems. The direct derivation from the definitions of LHV models and the requirement to reproduce every projective measurement is parameter-free and avoids fitted parameters or self-referential assumptions. The explicit comparison with restricted measurement sets usefully illustrates how the universal quantifier over measurements changes the picture, and the handling of deterministic outcomes and relabeling under communication is a clear strength.

minor comments (2)

Abstract: the phrase 'two bits of classical communication can explain the correlations of any two-qubit state' would benefit from a brief parenthetical clarifying whether this refers to one-way or two-way communication, to set up the subsequent restriction to outcome communication.
The manuscript should include an explicit early definition or diagram distinguishing 'outcome communication' from general classical communication, as the distinction is load-bearing for the later claims about relabeling.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their supportive summary and for recognizing the significance of our equivalence result for qubit-qudit states under all projective measurements. We appreciate the recommendation of minor revision.

Circularity Check

0 steps flagged

No significant circularity; direct mathematical equivalence from definitions

full rationale

The central result is an if-and-only-if statement: a qubit-qudit state admits an LHV model with outcome communication that reproduces all projective measurements if and only if it admits an ordinary LHV model without communication. This equivalence is derived from the model definitions together with the universal quantifier over all projective measurements, and the paper explicitly contrasts it with finite or restricted measurement sets where communication does provide an advantage. No parameters are fitted, no predictions are renamed fits, and no load-bearing self-citations or imported uniqueness theorems appear in the derivation chain. The logical structure is internally consistent and self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the standard definitions of local hidden variable models, the quantum formalism for qubit-qudit states, and the distinction between projective measurements and restricted measurement sets. No free parameters or new entities are introduced.

axioms (2)

domain assumption Standard definition of local hidden variable (LHV) models
Used to define both the no-communication and outcome-communication scenarios throughout the argument.
standard math Quantum mechanics description of qubit-qudit states and projective measurements
Provides the correlations that the models must reproduce.

pith-pipeline@v0.9.0 · 5760 in / 1152 out tokens · 34044 ms · 2026-05-18T07:15:41.662659+00:00 · methodology

discussion (0)

Reference graph

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M. Besançon, A. Carderera, and S. Pokutta, Frank- Wolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients, arXiv e-prints , arXiv:2104.06675 (2021). 8 APPENDIX PROOF OF THEOREM 1 Theorem 1.Letp(ab|xy)be a nonsignalling behaviour where Alice’s outcomes are dichotomic(a∈ {±1}). Sup- pose thatp(ab|xy)admits an L...

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[49]

nX y=1 X x:ax=+1 Mxyby,+1 − mX y=1 X x:ax=−1 Mxyby,−1 # = max ⃗ a∈{−1,1}n ⃗b∈{−1,1}n×2

The casep A(−1|x′) = 1is analogous. Sincep(ab|xy)admits an LHV+Out model, we have p(ab|xy) = X λ p(λ)pA(a|xλ)pB(b|ayλ),∀a, b, x, y.(4) We claim thatp(ab|xy)admits the following LHV model: p(ab|xy) = X λ p(λ)pA(a|xλ)epB(b|yλ),∀a, b, x, y.(5) wherep(λ)andp A(a|xλ)are the same as in Eq. (4), and epB(b|yλ) :=p B(b|1yλ)∀b, y, λ. Fora= 1, Eq. (4) dir- ectly imp...

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[50]

Divide the weightp(λ)of each strategy by two

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[51]

/werner_nomarg_sqrt2.dat

In the duplicated strategies, flip the signs of all outcomes⟨aλ x⟩,⟨b λ y,−1⟩, and⟨b λ y,+1⟩. Our model is stored in the filewerner_nomarg_sqrt2.datand has four components:as,bms,bps, andweights. These correspond, respectively, to Alice’s and Bob’s deterministic assignments, and the probability distribution over the hidden variables. Let us load the model...

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