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arxiv: 2604.27173 · v2 · submitted 2026-04-29 · 🪐 quant-ph

Quantum Coordination without Conditioning under Restricted Information

Faisal Shah Khan This is my paper

Pith reviewed 2026-05-08 03:03 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum coordinationrestricted informationquantum discordseparable stateslatent variablesclassical local models
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The pith

Quantum separable states with discord enable joint distributions that classical local models cannot achieve when agents cannot condition on past history.

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

The paper demonstrates that under information restrictions preventing conditioning on past outcomes, quantum systems can realize certain correlated behaviors using only separable states. This works through shared latent variables encoded diagonally or via noncommuting local structures in states with quantum discord. A sympathetic reader would care because it shows quantum resources can partially replace the need for perfect recall in coordination tasks. The models succeed where classical ones fail by allowing coordination without direct access to the latent information.

Core claim

Both classically diagonal encodings and separable states with noncommuting local structure enable the implementation of joint distributions unattainable by classical local rules under the same restricted information constraints. The quantum advantage arises from enabling latent-variable coordination without requiring agents to condition on the latent variable itself. Quantum models remain strictly limited by the information structure and cannot reproduce fully adaptive dependence on realized past outcomes that are observationally indistinguishable.

What carries the argument

Separable states with nonzero quantum discord, which provide noncommuting local structure allowing latent-variable coordination without agents conditioning on the latent variable.

If this is right

  • Quantum models implement joint distributions beyond those possible with any classical local rules under identical information constraints.
  • These quantum constructions succeed by enabling coordination via latent variables without direct conditioning on them.
  • Quantum approaches stay bounded by the information structure and cannot achieve fully adaptive dependence on observationally indistinguishable past outcomes.
  • Separable states with discord provide a distinct mechanism from entangled states for realizing the coordination.

Where Pith is reading between the lines

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

  • This mechanism may extend to designing quantum protocols for distributed tasks where agents have limited memory of prior events.
  • Testing whether zero-discord separable states lose the coordination capability would confirm the role of noncommuting local structure.
  • The results connect to broader questions of when quantum resources substitute for memory in information-constrained settings.

Load-bearing premise

The defined restricted information structure precisely captures the inability of agents to condition on past history without the quantum models implicitly permitting such conditioning through measurements or state structure.

What would settle it

A classical local model that implements the same joint distributions when agents are strictly forbidden from conditioning on past history would falsify the quantum advantage claim.

Figures

Figures reproduced from arXiv: 2604.27173 by Faisal Shah Khan.

Figure 1
Figure 1. Figure 1: Tree representation of the binary illustrative example. The dashed line indicates that the two second-step nodes are indistinguishable under the available view at source ↗
read the original abstract

We study coordination under restricted information, where classical local models fail to implement certain correlated distributions because agents cannot condition on past history. We show that quantum systems overcome this limitation even when using only separable states. Both classically diagonal encodings (shared latent variables) and separable states with noncommuting local structure (quantum discord) enable the implementation of joint distributions that are unattainable by any classical local rules under the same information constraints. The quantum advantage arises from enabling latent-variable coordination without requiring agents to condition on the latent variable itself -- a construction that succeeds where no classical local model can. Separable states with nonzero quantum discord provide an alternative mechanism for realizing such coordination. At the same time, quantum models remain strictly limited by the information structure: unlike perfect recall, they cannot reproduce fully adaptive dependence on realized past outcomes that are observationally indistinguishable. Thus, quantum correlations serve as a partial substitute for perfect recall.

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

2 major / 2 minor

Summary. The manuscript claims that under restricted information constraints (where agents cannot condition on past history or latent variables), certain joint distributions are unattainable by classical local models, but can be realized using quantum separable states with nonzero discord. This quantum advantage stems from enabling latent-variable coordination without explicit conditioning on the latent variable itself, while quantum models remain strictly limited and cannot reproduce fully adaptive dependence on observationally indistinguishable past outcomes.

Significance. If the central claims are supported by explicit constructions and proofs, the result would establish a concrete quantum advantage in coordination tasks under information restrictions, using discord as a substitute for classical conditioning. This could inform quantum distributed computing and information theory by clarifying boundaries between quantum correlations and perfect recall.

major comments (2)
  1. [Abstract (and presumed Section 2 on model definitions)] The load-bearing distinction between classical local rules and quantum separable states with discord requires explicit side-by-side formalization of the allowed operations under the restricted information structure. The abstract asserts that noncommuting local structure does not implicitly permit conditioning, but without a precise definition of the information constraints (e.g., what measurements or state preparations are permitted), it is unclear whether the quantum models satisfy the same restrictions as the classical ones.
  2. [Abstract] No concrete example, theorem, or derivation is supplied in the provided abstract showing a specific joint distribution unattainable classically but achievable quantumly. The claim that 'both classically diagonal encodings and separable states with noncommuting local structure enable...' needs at least one worked example with the exact probability distributions and information constraints listed.
minor comments (2)
  1. [Abstract] The abstract introduces terms such as 'classically diagonal encodings' and 'quantum discord' without inline definitions or citations to standard references (e.g., Ollivier-Zurek discord).
  2. [Abstract] Clarify the precise sense in which quantum models 'cannot reproduce fully adaptive dependence' to avoid ambiguity with the positive claims about partial substitution for recall.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting areas where additional clarity would strengthen the presentation. We address each major comment below and have revised the manuscript to incorporate explicit clarifications and examples while preserving the original technical content.

read point-by-point responses

  1. Referee: [Abstract (and presumed Section 2 on model definitions)] The load-bearing distinction between classical local rules and quantum separable states with discord requires explicit side-by-side formalization of the allowed operations under the restricted information structure. The abstract asserts that noncommuting local structure does not implicitly permit conditioning, but without a precise definition of the information constraints (e.g., what measurements or state preparations are permitted), it is unclear whether the quantum models satisfy the same restrictions as the classical ones.

    Authors: We agree that the abstract is concise and that a side-by-side comparison aids readability. Section 2 of the full manuscript already defines the restricted information structure identically for both models: agents may prepare states or perform local measurements but cannot condition on realized past outcomes or latent variables. The quantum model uses separable states (possibly with discord) under precisely these constraints, with no additional conditioning permitted by noncommuting operators. To make this explicit, we have added a clarifying sentence to the abstract and inserted a comparison table (Table 1) in the revised manuscript that lists permitted operations for classical local rules versus quantum separable states. revision: yes

  2. Referee: [Abstract] No concrete example, theorem, or derivation is supplied in the provided abstract showing a specific joint distribution unattainable classically but achievable quantumly. The claim that 'both classically diagonal encodings and separable states with noncommuting local structure enable...' needs at least one worked example with the exact probability distributions and information constraints listed.

    Authors: The abstract summarizes the central result; the explicit constructions, theorem statements, and a worked example (a three-outcome coordination distribution with specific probabilities unattainable by classical local rules under no-history conditioning but realized by a separable state with discord) appear in Sections 3 and 4. We have now included a brief version of this example, with the target joint distribution and the exact information constraints, directly in the revised abstract to address the concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines restricted information as the inability of agents to condition on past history or latent variables, then shows that classical local models cannot realize certain joint distributions under this constraint while separable quantum states with discord can. This comparison relies on the formal properties of commuting vs. noncommuting observables and the definition of quantum discord, without any quoted equations or self-citations that reduce the claimed advantage to a tautology, fitted parameter, or prior result by the same authors. No self-definitional loops, renamed known results, or ansatzes smuggled via citation appear in the abstract or described chain. The result is presented as an independent demonstration that quantum models provide a partial substitute for perfect recall, remaining strictly limited by the same information structure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the claim rests on standard assumptions from quantum information theory and classical coordination models; no free parameters, invented entities, or ad-hoc axioms are explicitly introduced in the provided text.

axioms (2)
  • domain assumption Classical local models fail to implement certain correlated distributions when agents cannot condition on past history.
    Directly stated as the starting limitation in the abstract.
  • standard math Separable quantum states can exhibit noncommuting local observables that produce quantum discord.
    Invokes established quantum information concepts without further justification in the abstract.

pith-pipeline@v0.9.0 · 5436 in / 1195 out tokens · 116010 ms · 2026-05-08T03:03:30.782899+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

  1. [1]

    Extensive games and the problem of information,

    H. W. Kuhn, “Extensive games and the problem of information,”Contributions to the Theory of Games II, vol. 28, pp. 193–216, 1953

    work page 1953

  2. [2]

    M. J. Osborne and A. Rubinstein,A Course in Game Theory. MIT Press, 1994

    work page 1994

  3. [3]

    Games with incomplete information played by “bayesian

    J. C. Harsanyi, “Games with incomplete information played by “bayesian” players, part i: The basic model,”Management Science, vol. 14, no. 3, pp. 159–182, 1967

    work page 1967

  4. [4]

    Games with incomplete information played by “bayesian

    ——, “Games with incomplete information played by “bayesian” players, parts ii and iii,”Management Science, vol. 14, no. 5, pp. 320–334, 1968

    work page 1968

  5. [5]

    Distributed quantum error mitigation: Global and local zne encodings,

    M. Gragera Garces, “Distributed quantum error mitigation: Global and local zne encodings,”arXiv preprint arXiv:2602.04981, 2026

    work page arXiv 2026

  6. [6]

    Quantum discord: A measure of the quantumness of correlations,

    H. Ollivier and W. H. Zurek, “Quantum discord: A measure of the quantumness of correlations,”Physical Review Letters, vol. 88, no. 1, p. 017901, 2001

    work page 2001

  7. [7]

    Classical, quantum and total correlations,

    L. Henderson and V . Vedral, “Classical, quantum and total correlations,”Journal of Physics A: Mathematical and General, vol. 34, no. 35, pp. 6899–6905, 2001

    work page 2001

  8. [8]

    Quantum discord and the power of one qubit,

    A. Datta, A. Shaji, and C. M. Caves, “Quantum discord and the power of one qubit,”Physical Review Letters, vol. 100, no. 5, p. 050502, 2008

    work page 2008

  9. [9]

    The classical-quantum boundary for correlations: Discord and related measures,

    K. Modi, A. Brodutch, H. Cable, T. Paterek, and V . Vedral, “The classical-quantum boundary for correlations: Discord and related measures,”Reviews of Modern Physics, vol. 84, no. 4, pp. 1655–1707, 2012

    work page 2012

  10. [10]

    Quantum games and quantum strategies,

    J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,”Physical Review Letters, vol. 83, no. 15, pp. 3077–3080, 1999

    work page 1999

  11. [11]

    Team decision problems with classical and quantum signals,

    A. Brandenburger and P. La Mura, “Team decision problems with classical and quantum signals,”Philosophical Transactions of the Royal Society A, vol. 374, no. 2058, p. 20150096, 2016

    work page 2058

  12. [12]

    Team decision problems with classical and quantum signals,

    A. Brandenburger and P. L. Mura, “Team decision problems with classical and quantum signals,”Games and Economic Behavior, vol. 71, no. 1, pp. 123–134, 2011

    work page 2011

  13. [13]

    Quantum game players can have advantage without discord,

    Z. Wei and S. Zhang, “Quantum game players can have advantage without discord,”Information and Computation, vol. 256, pp. 174–184, 2017

    work page 2017

  14. [14]

    When recall fails, discord remembers: A quantum analogue of kuhn’s theorem,

    F. S. Khan, “When recall fails, discord remembers: A quantum analogue of kuhn’s theorem,”Quantum Economics and Finance, vol. 2, no. 2, pp. 141–147, 2025

    work page 2025