Pith. sign in

REVIEW 2 major objections 4 minor 63 references

In any generalized probabilistic theory, a set of states that provides an advantage in a contextuality-powered task must obey strict upper bounds on the success probability of every state-discrimination task using that set, so contextual ad

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review

2026-08-01 00:40 UTC pith:TMEFFWIM

load-bearing objection A solid GPT-level trade-off between state discrimination and contextual advantage, with one definitional gap that needs patching. the 2 major comments →

arxiv 2607.26145 v1 pith:TMEFFWIM submitted 2026-07-28 quant-ph

Contextual advantage implies limited distinguishability in any physical theory

Roberto D. Baldij\~{a}o , Felipe A. Barretto , Jaros\l{}aw K. Korbicz This is my paper
classification quant-ph PACS 03.67.-a
keywords generalized probabilistic theoriesstate discriminationgeneralized contextualitylinear dependencenoncontextual modelsprepare-and-measure scenariosparity-oblivious multiplexingoperational resources
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.

This paper establishes a universal trade-off in any physical theory of the generalized probabilistic type: if a set of states can deliver an advantage in a task whose power comes from 'contextuality'—the failure of a classical, noncontextual explanation—then those same states cannot be too easy to tell apart. Concretely, the optimal success probability in any state-discrimination task that uses all the states is bounded strictly below 1, with a bound computed from the prior probabilities and the convex geometry of the state set. The engine is linear dependence: linearly independent states always admit a noncontextual model, so any contextually advantageous set must be linearly dependent, and linear dependence directly caps discrimination success. A sympathetic reader should care because this links two fundamental operational resources—contextuality, a known resource for quantum advantages, and distinguishability—and yields practical feasibility tests for state sets in any GPT without solving the hard discrimination optimization.

Core claim

The paper's central claim is Theorem 2: in any GPT, if a set of states {s_k} provides advantage in some contextuality-powered task, then for every state-discrimination task using the whole set (with positive priors p_k), the guessing probability obeys P_guess ≤ 1 − P_{q} for every linearly independent decomposition q of the average state; hence P_guess ≤ 1 − max_q P_q ≤ 1 − p_min/2. This follows from two ingredients: Lemma 1 says a linearly independent set cannot exhibit prepare-and-measure contextuality (it admits a noncontextual ontological model), and Theorem 1 says any linearly dependent set has P_guess bounded strictly below 1, with the bound depending only on the priors and the convex

What carries the argument

The engine is linear (in)dependence of the state set, combined with a convex-geometric quantity: for an average state \bar{s}, any linearly independent subset spanning it gives a decomposition q with weights differing from the prior p by total-variation distance V(q,p). The bound P_{q} = p_min (1 + p_min/V(q,p))^{-1} converts that geometric difference into an upper bound on guessing probability. Lemma 1 supplies the physical bridge: linearly independent states can be given a noncontextual model (using the states themselves as hidden variables), so any state set with contextual power must be linearly dependent.

Load-bearing premise

The argument assumes that any task whose advantage 'stems from generalized contextuality' necessarily uses a state set that is itself contextual, so that advantage implies the set is linearly dependent by the contrapositive of Lemma 1; if such an advantage could arise from measurement contextuality alone without the state set being contextual, the chain from advantage to linear dependence—and hence to the discrimination bounds—would break.

What would settle it

Find a GPT state set that is linearly dependent but achieves P_guess = 1 for some full-set state-discrimination task (violating Theorem 1), or identify a task generally accepted as contextuality-powered whose advantage can be realized with a linearly independent state set (violating Theorem 2). Concretely, scan small GPTs (e.g., the gbit or rebit) for ensembles whose optimal discrimination success exceeds 1 − max_q P_q; the first such ensemble would refute the paper's central claim.

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

Share X LinkedIn Reddit HN

If this is right

  • In any GPT, every linearly dependent state set has state-discrimination success bounded strictly below 1 for every full-set SD task; the bound is computable from just the priors and the convex geometry.
  • Any state set whose discrimination success beats the bound (e.g., P_guess > 1 − p_min/2) is guaranteed noncontextual: every prepare-and-measure experiment using that set admits a classical explanation, so it cannot power contextual advantage.
  • The bounds are invariant under injective linear maps, so they constrain not one state set but every linearly equivalent realization, across different GPTs (qubit, gbit, rebit, etc.).
  • For uniform priors the bound simplifies to 1 − (1/N)(N−D)/(N−D+1), depending only on the number of states and the dimension of their span.
  • In a d-ary oblivious multiplexing task, if the overall success exceeds 1 − 1/(2d), at least one sub-ensemble of the codebook cannot provide advantage in any contextuality-powered task.

Where Pith is reading between the lines

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

  • A testable extension: the bounds suggest a quantitative witness—prepare a hypothesized contextual state set, measure its optimal discrimination success, and compare against 1 − p_min/2; exceeding the bound would certify that the set cannot underlie any contextuality-powered advantage, checkable in tabletop experiments.
  • The framework implies that protocols exploiting contextuality as a resource must tolerate imperfectly distinguishable encodings; error-correction or amplification steps that boost distinguishability may inadvertently destroy the contextual resource.
  • The paper leaves 'contextuality-powered task' informal; formalizing it as tasks whose optimal success exceeds what any noncontextual model allows would turn Theorem 2 into a fully constructive criterion.
  • The bounds are universal but not tight; in quantum theory, stronger limits may hold, and systematic searches over small GPT state sets could reveal whether contextuality imposes even harsher discrimination ceilings than linear dependence alone.

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

2 major / 4 minor

Summary. The paper studies state discrimination in generalized probabilistic theories (GPTs) and derives upper bounds on the optimal guessing probability P_guess from a purely geometric property: linear dependence of the state set. Theorem 1 and its corollaries give closed-form bounds that depend only on the prior distribution and on weights of linearly independent decompositions of the average state. Corollary 2 proves invariance of these bounds under injective linear maps, so they apply to equivalence classes of GPT state sets. Lemma 1 shows that a linearly independent set of GPT states cannot give rise to prepare-and-measure contextuality. The main conceptual result, Theorem 2, then states that any set of states providing advantage in a 'contextuality-powered' task must satisfy the SD bounds of Theorem 1 in every state-discrimination task using the full set. The paper applies these ideas to generalized parity-oblivious multiplexing, showing that high success in such tasks forces at least one sub-ensemble to be classically explainable. Proofs for the main results are given in the appendices, together with strengthened bounds for uniform priors and non-extremal states.

Significance. If the main claim holds, it establishes a genuinely universal trade-off between two operational resources: generalized contextuality and state discriminability. The result is theory-independent, applies to quantum and non-quantum GPTs, and has a surprisingly simple geometric origin. A notable strength is that the core derivations of Theorem 1, Corollaries 1 and 4, and Lemma 1 are self-contained and do not rely on fitted parameters or hidden assumptions beyond standard GPT axioms. The invariance under injective linear maps is a clean and useful observation. However, the central conceptual theorem depends on an unformalised notion of 'contextuality-powered task', and one of the appendix refinements (Lemma 4) has a proof gap. These issues are local and likely repairable, but they currently block acceptance.

major comments (2)
  1. [§IV (Theorem 2)] The central term 'contextuality-powered task' is never formally defined. The proof of Theorem 2 requires the implication: if {s_k} provides advantage in such a task, then the prepare-and-measure fragment ({s_k}, E, B) is contextual, so that the contrapositive of Lemma 1 applies. Under the standard reading — a task whose success probability exceeds the maximum allowed by noncontextual ontological models for that fragment — the step is valid, but the manuscript should state this reading explicitly and explain why an advantage in such a task implies contextuality of the state set. As written, Theorem 2 is a meta-theorem with an informal premise, and this premise is load-bearing for the paper's main conceptual claim.
  2. [Appendix A 2 (Lemma 4)] In the proof of Lemma 4, Eq. (A31) is identified with 'the error probability of the state discrimination task (q_i,s_i)_{i∈Q+}' for a potentially non-optimal measurement. This is not correct: the sum over k∈Q+ omits outcomes k∉Q+ and the complement effect u−Σ_{k∈Q+}e_k, so (A31) is only a partial contribution to the error. It therefore need not be ≥ P^S_error. Consequently the derivation of Lemma 4 and the numerical bound in Example 2 relying on it are not supported as written. The lemma may be true, but the proof needs to be repaired or the lemma removed/restated as a conditional result.
minor comments (4)
  1. [Throughout] Several typos and wording issues: 'ADVANT AGE' in the Section IV heading, 'gOM taks' in Example 1, and inconsistent use of 'contextually-powered' vs 'contextuality-powered'.
  2. [Appendix A 5 / Corollary 3] Eq. (11) uses a strict inequality '<' for P_guess, but the proof via Corollary 4 provides '≤'. Please justify the strictness or state the non-strict inequality unless an additional argument rules out equality.
  3. [Theorem 1] The notation P_{qk} in Eq. (4) is easy to confuse with P_guess; a more explicit notation, such as P_q(V), would improve readability.
  4. [Example 2] The statement that 'any antipodal pair' gives a linearly independent decomposition of the cube center is correct only because the center is a normalized state and hence nonzero; adding a parenthetical clarifying why the center is nonzero would help avoid confusion.

Circularity Check

0 steps flagged

No significant circularity: the SD bounds are derived from GPT axioms and independent noncontextuality characterizations, and Theorem 2 is a straightforward contrapositive.

full rationale

The paper's central derivation is self-contained conditional on standard GPT axioms and on the external, non-author noncontextuality characterizations of Refs. [20,29]. Theorem 1 is proved in Appendix A.1 from Lemmas 2 and 3 using only bilinearity, the nondegenerate probability rule, and elementary convex-geometric decomposition facts; no parameter is fitted to the SD probabilities being bounded, and the bound is not a relabeling of P_guess. Lemma 1 is proved in Appendix A.4 by constructing an explicit simplex embedding of the fragment ({s_k}, E, B), using the equivalence between noncontextuality and simplex-embeddability proved in independent work (Refs. [20,29]; the author lists of those references do not include the present authors). Theorem 2 is then a direct contrapositive: contextual advantage excludes linear independence by Lemma 1, so Theorem 1 applies. The self-citations in the paper (Refs. [17,28,45,50]) appear mainly for conventions, notation, or illustrative quantum-Darwinism context and are not load-bearing for the main proof. The only genuine soft spot is that 'contextuality-powered task' is never formally defined; if it is read in the standard way as a task whose success probability exceeds the maximum achievable by a noncontextual model of the prepare-and-measure fragment, the implication 'contextual advantage implies linear dependence' is valid. This is a definitional-precision gap rather than a circular reduction: no equation in the paper is equal to its input by construction, and no fitted quantity is renamed as a prediction. Therefore the circularity score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The central claim rests on the standard GPT axioms (Section II.A), on external theorems about noncontextuality and simplex embeddings (Refs [20,29]), on Carathéodory's theorem, and on the informal premise that 'contextuality-powered' tasks require contextual states. There are no free parameters and no invented entities; all bounds are derived analytically.

axioms (6)
  • domain assumption GPT framework axioms: compact convex normalized state set Ω̄, closed convex effect space E, bilinear probability rule B, deterministic effect u with u−e∈E, nondegenerate separation.
    Section II.A adopts these as the definition of a GPT system; all theorems are proven within this framework, so the results inherit its scope.
  • domain assumption Normalized states lie on an affine hyperplane not containing the origin, making linear independence coincide with affine independence for state sets.
    Section II.A; used in Remark 1 and throughout to justify translating affine decompositions into linear ones and to apply Carathéodory's theorem.
  • standard math Carathéodory's theorem: any point in the convex hull of a set in affine dimension d is a convex combination of at most d+1 affinely independent points.
    Used in Remark 1 to guarantee existence of a linearly independent decomposition of the average state; also used to ensure a zero-coefficient decomposition in Corollary 1.
  • domain assumption Noncontextuality of a GPT fragment is equivalent to simplex-embeddability into a strictly classical (simplicial) GPT.
    External theorem from Refs [20,29], invoked in the proof of Lemma 1 (Appendix A4) to conclude linear independence implies a noncontextual model.
  • standard math Nondegeneracy of B implies the maximal effect set E_max on the simplex Ω' is isomorphic to the full dual simplex.
    Used in Lemma 1's proof to construct the embedding of effects into Δ*; follows from the separation property stated in Section II.A.
  • domain assumption A 'contextuality-powered task' is one whose advantage cannot be reproduced by any noncontextual model of the states involved.
    Theorem 2 (Section IV) and Example 1 rely on this to infer that advantage implies the state set is contextual, and hence linearly dependent by Lemma 1's contrapositive. This is a definitional bridge the paper does not formalize.

reviewed 2026-08-01 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Contextual advantage implies limited distinguishability in any physical theory." pith.science (2026). https://pith.science/paper/TMEFFWIM

@misc{pith2026260726145,
  author       = {Pith},
  title        = {Pith review of: Contextual advantage implies limited distinguishability in any physical theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TMEFFWIM}},
  note         = {Machine review of arXiv:2607.26145}
}
Share X LinkedIn Reddit HN
read the original abstract

A central question in quantum information is whether a given set of states can provide an advantage in some information-processing task. We establish a universal connection between two such questions: how well a set of states can be discriminated, and whether it can power tasks whose advantage stems from generalized contextuality. Working in the framework of generalized probabilistic theories (GPTs), which includes quantum and classical systems as special cases, we show that any set of states able to provide a nonclassical advantage in a contextuality-powered task must obey nontrivial upper bounds on the success probability of every state discrimination task using the full set. Contextual advantage therefore implies limited distinguishability, exposing a trade-off between two basic operational resources. Importantly, this is more than a statement about the idealized limit: perfect distinguishability is not needed to preclude contextuality. Our thresholds lie strictly below unity, so any set whose discrimination performance exceeds them while still imperfectly distinguishable is already guaranteed to admit a noncontextual explanation. The bounds follow from a simple geometric property, linear dependence of the state set, take a closed analytical form, and depend only on the prior of the task and the convex geometry of the states. As an illustration, we apply them to generalized parity-oblivious multiplexing, where sufficiently high success in the task implies that at least one sub-ensemble of the codebook cannot power any contextual advantage.

Figures

Figures reproduced from arXiv: 2607.26145 by Felipe A. Barretto, Jaros\l{}aw K. Korbicz, Roberto D. Baldij\~{a}o.

Figure 1
Figure 1. Figure 1: FIG. 1: A prepare-and-measure scenario. A preparation [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Two GPT systems with state and effect spaces [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Consider an SD task for the rebit state space, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Illustration of Corollary [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

63 extracted references · 16 canonical work pages

  1. [1]

    real state of affairs

    The resulting bounds are straightforward to compute, relying only on the convex geometry of the state set, and can be used to assess whether a target discrimination performance is feasible for a given set of states. Useful as these bounds might be on their own, their most significant consequence emerges only later, once we connect them to generalized cont...

    Pith/arXiv arXiv 2026

  2. [2]

    Structure of minimum-error quantum state discrimination.New Journal of Physics, 15(7):073037, July 2013

    Joonwoo Bae. Structure of minimum-error quantum state discrimination.New Journal of Physics, 15(7):073037, July 2013. ISSN 1367-2630. doi:10.1088/1367-2630/15/7/073037. URL http://dx.doi.org/10.1088/1367-2630/15/7/073037

    work page doi:10.1088/1367-2630/15/7/073037 2013

  3. [3]

    Structure of optimal state discrimination in generalized probabilistic theories.Entropy, 18(2):39, January 2016

    Joonwoo Bae, Dai-Gyoung Kim, and Leong-Chuan Kwek. Structure of optimal state discrimination in generalized probabilistic theories.Entropy, 18(2):39, January 2016. ISSN 1099-4300. doi:10.3390/e18020039. URLhttp://dx.doi.org/10.3390/e18020039

    work page doi:10.3390/e18020039 2016

  4. [4]

    Quantum state discrimination and selected applications.J

    J´ anos A Bergou. Quantum state discrimination and selected applications.J. Phys. Conf. Ser., 84:012001, October 2007

    2007

  5. [5]

    Barnett and Sarah Croke

    Stephen M. Barnett and Sarah Croke. Quantum state discrimination, 2008. URLhttps://arxiv.org/abs/ 0810.1970

    Pith/arXiv arXiv 2008

  6. [6]

    Probabilistic theories and reconstructions of quantum theory.SciPost Physics Lecture Notes, March 2021

    Markus M¨ uller. Probabilistic theories and reconstructions of quantum theory.SciPost Physics Lecture Notes, March 2021. ISSN 2590-1990. doi:10.21468/scipostphyslectnotes.28. URLhttp: //dx.doi.org/10.21468/SciPostPhysLectNotes.28

    doi:10.21468/scipostphyslectnotes.28 2021

  7. [7]

    Information processing in generalized probabilistic theories, 2006

    Jonathan Barrett. Information processing in generalized probabilistic theories, 2006. URLhttps://arxiv.org/ abs/quant-ph/0508211

    Pith/arXiv arXiv 2006

  8. [8]

    General probabilistic theories: An introduction.Physics Reports, 1033: 1–64, September 2023

    Martin Pl´ avala. General probabilistic theories: An introduction.Physics Reports, 1033: 1–64, September 2023. ISSN 0370-1573. doi:10.1016/j.physrep.2023.09.001. URLhttp: //dx.doi.org/10.1016/j.physrep.2023.09.001. 10

    doi:10.1016/j.physrep.2023.09.001 2023

  9. [9]

    Springer Netherlands, 2016

    Giulio Chiribella, Giacomo Mauro D’Ariano, and Paolo Perinotti.Quantum Theory: Informational Foundations and Foils. Springer Netherlands, 2016. ISBN 9789401773034. doi:10.1007/978-94-017-7303-4. URL http://dx.doi.org/10.1007/978-94-017-7303-4

    doi:10.1007/978-94-017-7303-4 2016

  10. [10]

    Reformulating and reconstructing quantum theory, 2011

    Lucien Hardy. Reformulating and reconstructing quantum theory, 2011. URLhttps://arxiv.org/abs/ 1104.2066

    Pith/arXiv arXiv 2011

  11. [11]

    Quantum theory from five reasonable axioms, 2001

    Lucien Hardy. Quantum theory from five reasonable axioms, 2001

    2001

  12. [12]

    A derivation of quantum theory from physical requirements.New Journal of Physics, 13(6):063001, June 2011

    Llu ´ ıs Masanes and Markus P M¨ uller. A derivation of quantum theory from physical requirements.New Journal of Physics, 13(6):063001, June 2011. ISSN 1367-2630. doi:10.1088/1367-2630/13/6/063001. URL http://dx.doi.org/10.1088/1367-2630/13/6/063001

    doi:10.1088/1367-2630/13/6/063001 2011

  13. [13]

    Probabilistic theories with purification

    Giulio Chiribella, Giacomo Mauro D’Ariano, and Paolo Perinotti. Probabilistic theories with purification. Physical Review A, 81(6), June 2010. ISSN 1094-1622. doi:10.1103/physreva.81.062348. URLhttp://dx.doi. org/10.1103/PhysRevA.81.062348

    doi:10.1103/physreva.81.062348 2010

  14. [14]

    M¨ uller and Cozmin Ududec

    Markus P. M¨ uller and Cozmin Ududec. Structure of reversible computation determines the self-duality of quantum theory.Physical Review Letters, 108(13), March 2012. ISSN 1079-7114. doi:10.1103/physrevlett.108.130401. URLhttp: //dx.doi.org/10.1103/PhysRevLett.108.130401

    work page doi:10.1103/physrevlett.108.130401 2012

  15. [15]

    Strongly symmetric spectral convex bodies are jordan algebra state spaces, 2019

    Howard Barnum and Joachim Hilgert. Strongly symmetric spectral convex bodies are jordan algebra state spaces, 2019. URLhttps://arxiv.org/abs/1904. 03753

    2019

  16. [16]

    Higher-order interference and single-system postulates characterizing quantum theory.New Journal of Physics, 16(12):123029, December 2014

    Howard Barnum, Markus P M¨ uller, and Cozmin Ududec. Higher-order interference and single-system postulates characterizing quantum theory.New Journal of Physics, 16(12):123029, December 2014. ISSN 1367-2630. doi:10.1088/1367-2630/16/12/123029. URLhttp://dx. doi.org/10.1088/1367-2630/16/12/123029

    doi:10.1088/1367-2630/16/12/123029 2014

  17. [17]

    An information-theoretic principle implies that any discrete physical theory is classical.Nat

    Corsin Pfister and Stephanie Wehner. An information-theoretic principle implies that any discrete physical theory is classical.Nat. Commun., 4(1):1851, 2013

    2013

  18. [18]

    Baldijao, Marius Krumm, Andrew J

    Roberto D. Baldijao, Marius Krumm, Andrew J. P. Garner, and Markus P. Mueller. Quantum darwinism and the spreading of classical information in non-classical theories.Quantum, 6:636, January 2022. ISSN 2521-327X. doi:10.22331/q-2022-01-31-636. URLhttp: //dx.doi.org/10.22331/q-2022-01-31-636

    work page doi:10.22331/q-2022-01-31-636 2022

  19. [19]

    R. W. Spekkens. Contextuality for preparations, transformations, and unsharp measurements.Physical Review A, 71(5), May 2005. ISSN 1094-1622. doi:10.1103/physreva.71.052108. URLhttp://dx.doi. org/10.1103/PhysRevA.71.052108

    doi:10.1103/physreva.71.052108 2005

  20. [20]

    Spekkens

    Robert W. Spekkens. Negativity and contextuality are equivalent notions of nonclassicality.Physical Review Letters, 101(2), July 2008. ISSN 1079-7114. doi:10.1103/physrevlett.101.020401. URLhttp://dx. doi.org/10.1103/PhysRevLett.101.020401

    doi:10.1103/physrevlett.101.020401 2008

  21. [21]

    Selby, Elie Wolfe, Ravi Kunjwal, and Robert W

    David Schmid, John H. Selby, Elie Wolfe, Ravi Kunjwal, and Robert W. Spekkens. Characterization of noncontextuality in the framework of generalized probabilistic theories. PRX Quantum, 2(1), February 2021. ISSN 2691-3399. doi:10.1103/prxquantum.2.010331. URL http://dx.doi.org/10.1103/PRXQuantum.2.010331

    doi:10.1103/prxquantum.2.010331 2021

  22. [22]

    John S. Bell. On the einstein podolsky rosen paradox.Physics Physique Fizika, 1(3):195–200, 1964. doi:10.1103/PhysicsPhysiqueFizika.1.195. URLhttps: //doi.org/10.1103/PhysicsPhysiqueFizika.1.195

    doi:10.1103/physicsphysiquefizika.1.195 1964

  23. [23]

    Simon Kochen and Ernst P. Specker. The problem of hidden variables in quantum mechanics.Journal of Mathematics and Mechanics, 17(1):59–87, 1967. URL https://www.jstor.org/stable/24902153

    arXiv 1967

  24. [24]

    Spekkens, D

    Robert W. Spekkens, D. H. Buzacott, A. J. Keehn, Ben Toner, and G. J. Pryde. Preparation contextuality powers parity-oblivious multiplexing. Phys. Rev. Lett., 102:010401, Jan 2009. doi:10.1103/PhysRevLett.102.010401. URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.102.010401

    doi:10.1103/physrevlett.102.010401 2009

  25. [25]

    Optimal bounds for parity-oblivious random access codes.New Journal of Physics, 18(4): 045003, apr 2016

    Andr´ e Chailloux, Iordanis Kerenidis, Srijita Kundu, and Jamie Sikora. Optimal bounds for parity-oblivious random access codes.New Journal of Physics, 18(4): 045003, apr 2016. doi:10.1088/1367-2630/18/4/045003. URLhttps://doi.org/10.1088/1367-2630/18/4/ 045003

    doi:10.1088/1367-2630/18/4/045003 2016

  26. [26]

    Contextuality supplies the magic for quantum computation.Nature, 510(7505):351–355, 2014

    Mark Howard, Joel Wallman, Victor Veitch, and Joseph Emerson. Contextuality supplies the magic for quantum computation.Nature, 510(7505):351–355, 2014. doi:10.1038/nature13460. URLhttps://doi.org/10. 1038/nature13460

    doi:10.1038/nature13460 2014

  27. [27]

    Contextuality in measurement-based quantum computation

    Robert Raussendorf. Contextuality in measurement-based quantum computation. Physical Review A, 88(2):022322, 2013. doi:10.1103/PhysRevA.88.022322. URLhttps: //doi.org/10.1103/PhysRevA.88.022322

    doi:10.1103/physreva.88.022322 2013

  28. [28]

    Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response.Physical Review Letters, 125(23), December 2020

    Matteo Lostaglio. Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response.Physical Review Letters, 125(23), December 2020. ISSN 1079-7114. doi:10.1103/physrevlett.125.230603. URLhttp: //dx.doi.org/10.1103/PhysRevLett.125.230603

    doi:10.1103/physrevlett.125.230603 2020

  29. [29]

    Selby, Vinicius P

    David Schmid, John H. Selby, Vinicius P. Rossi, Roberto D. Baldij˜ ao, and Ana Bel´ en Sainz. Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs.Quantum, 9:1880, October 2025. ISSN 2521-327X. doi:10.22331/q-2025-10-13-1880. URL http://dx.doi.org/10.22331/q-2025-10-13-1880

    doi:10.22331/q-2025-10-13-1880 2025

  30. [30]

    Selby, David Schmid, Elie Wolfe, Ana Bel´ en Sainz, Ravi Kunjwal, and Robert W

    John H. Selby, David Schmid, Elie Wolfe, Ana Bel´ en Sainz, Ravi Kunjwal, and Robert W. Spekkens. Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality.Physical Review A, 107(6), June 2023. ISSN 2469-9934. doi:10.1103/physreva.107.062203. URL http://dx.doi.org/10.1103/PhysRevA.107.062203

    doi:10.1103/physreva.107.062203 2023

  31. [31]

    Wootters

    William K. Wootters. Entanglement sharing in real-vector-space quantum theory.Foundations of Physics, 42(1):19–28, July 2010. ISSN 1572-9516. doi:10.1007/s10701-010-9488-1. URLhttp://dx.doi. org/10.1007/s10701-010-9488-1

    work page doi:10.1007/s10701-010-9488-1 2010

  32. [32]

    Limits on nonlocal correlations from the structure of the local state space.New Journal of Physics, 13(6):063024, June 2011

    Peter Janotta, Christian Gogolin, Jonathan Barrett, and Nicolas Brunner. Limits on nonlocal correlations from the structure of the local state space.New Journal of Physics, 13(6):063024, June 2011. ISSN 1367-2630. doi:10.1088/1367-2630/13/6/063024. URLhttp://dx. doi.org/10.1088/1367-2630/13/6/063024

    work page doi:10.1088/1367-2630/13/6/063024 2011

  33. [33]

    Deconinck and Barbara M

    Matthieu E. Deconinck and Barbara M. Terhal. Qubit state discrimination.Physical Review A, 81(6), June

  34. [34]

    Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities, 2021

    Donghoon Ha and Younghun Kwon. Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities, 2021. URL https://arxiv.org/abs/2111.07726

    Pith/arXiv arXiv 2021

  35. [35]

    Helstrom

    Carl W. Helstrom. Detection theory and quantum mechanics.Information and Control, 10(3):254–291,

  36. [36]

    pretty good

    Paul Hausladen and William K. Wootters. A “pretty good” measurement for distinguishing quantum states. Journal of Modern Optics, 41(12):2385–2390, 1994. doi:10.1080/09500349414552221. URLhttps://doi. org/10.1080/09500349414552221

    doi:10.1080/09500349414552221 1994

  37. [37]

    Reversing quantum dynamics with near-optimal quantum and classical fidelity.Journal of Mathematical Physics, 43(5): 2097–2106, 2002

    Howard Barnum and Emanuel Knill. Reversing quantum dynamics with near-optimal quantum and classical fidelity.Journal of Mathematical Physics, 43(5): 2097–2106, 2002. doi:10.1063/1.1459754. URLhttps: //doi.org/10.1063/1.1459754

    doi:10.1063/1.1459754 2097

  38. [38]

    Eldar, A

    Y.C. Eldar, A. Megretski, and G.C. Verghese. Designing optimal quantum detectors via semidefinite programming.IEEE Transactions on Information Theory, 49(4):1007–1012, 2003. doi:10.1109/TIT.2003.809510

    arXiv 2003

  39. [39]

    Spekkens

    Robert W. Spekkens. The ontological identity of empirical indiscernibles: Leibniz’s methodological principle and its significance in the work of einstein, 2019. URLhttps://arxiv.org/abs/1909.04628

    Pith/arXiv arXiv 2019

  40. [40]

    Browne, Cihan Okay, and Robert Raussendorf

    Juan Bermejo-Vega, Nicolas Delfosse, Dan E. Browne, Cihan Okay, and Robert Raussendorf. Contextuality as a resource for models of quantum computation with qubits.Phys. Rev. Lett., 119:120505, Sep 2017. doi:10.1103/PhysRevLett.119.120505. URLhttps:// doi.org/10.1103/PhysRevLett.119.120505

    doi:10.1103/physrevlett.119.120505 2017

  41. [41]

    Pretty simple bounds on quantum state discrimination, 2019

    Ashley Montanaro. Pretty simple bounds on quantum state discrimination, 2019. URLhttps://arxiv.org/ abs/1908.08312

    Pith/arXiv arXiv 2019

  42. [42]

    Selby, Matthew F

    David Schmid, John H. Selby, Matthew F. Pusey, and Robert W. Spekkens. A structure theorem for generalized-noncontextual ontological models.Quantum, 8:1283, March 2024. ISSN 2521-327X. doi:10.22331/q-2024-03-14-1283. URL http://dx.doi.org/10.22331/q-2024-03-14-1283

    work page doi:10.22331/q-2024-03-14-1283 2024

  43. [43]

    Baldij˜ ao, Y ` ıl` e Y ¯ ıng, Rafael Wagner, and John H

    David Schmid, Roberto D. Baldij˜ ao, Y ` ıl` e Y ¯ ıng, Rafael Wagner, and John H. Selby. Kirkwood-dirac representations beyond quantum states and their relation to noncontextuality.Physical Review A, 110(5), November 2024. ISSN 2469-9934. doi:10.1103/physreva.110.052206. URLhttp: //dx.doi.org/10.1103/PhysRevA.110.052206

    doi:10.1103/physreva.110.052206 2024

  44. [44]

    Spekkens

    David Schmid and Robert W. Spekkens. Contextual advantage for state discrimination.Phys. Rev. X, 8:011015, Feb 2018. doi:10.1103/PhysRevX.8.011015. URLhttps://link.aps.org/doi/10.1103/PhysRevX. 8.011015

    doi:10.1103/physrevx.8.011015 2018

  45. [45]

    Baldij˜ ao, Rafael Wagner, Cristhiano Duarte, B´ arbara Amaral, and Marcelo Terra Cunha

    Roberto D. Baldij˜ ao, Rafael Wagner, Cristhiano Duarte, B´ arbara Amaral, and Marcelo Terra Cunha. Emergence of noncontextuality under quantum darwinism.PRX Quantum, 2(3), September 2021. ISSN 2691-3399. doi:10.1103/prxquantum.2.030351. URLhttp://dx. doi.org/10.1103/PRXQuantum.2.030351

    work page doi:10.1103/prxquantum.2.030351 2021

  46. [46]

    Spekkens

    Yujie Zhang, David Schmid, Y ` ıl` e Y ¯ ıng, and Robert W. Spekkens. Reassessing the boundary between classical and nonclassical for individual quantum processes, 2026. URLhttps://arxiv.org/abs/2503.05884

    arXiv 2026

  47. [47]

    Comar, Danilo Cius, Luis F

    Naim E. Comar, Danilo Cius, Luis F. Santos, Rafael Wagner, and B´ arbara Amaral. Contextuality in anomalous heat flow.PRX Quantum, 6:030359, Sep

  48. [48]

    Fernando G. S. L. Brand˜ ao, Marco Piani, and Pawe l Horodecki. Generic emergence of classical features in quantum darwinism.Nature Communications, 6(1), August 2015. ISSN 2041-1723. doi:10.1038/ncomms8908. URLhttp://dx.doi.org/10.1038/ncomms8908

    work page doi:10.1038/ncomms8908 2015

  49. [49]

    Horodecki, J

    R. Horodecki, J. K. Korbicz, and P. Horodecki. Quantum origins of objectivity.Physical Review A, 91(3):032122, March 2015. ISSN 1094-1622. doi:10.1103/PhysRevA.91.032122. URLhttp://dx.doi. org/10.1103/PhysRevA.91.032122

    work page doi:10.1103/physreva.91.032122 2015

  50. [50]

    Jaros law K. Korbicz. Roads to objectivity: Quantum darwinism, spectrum broadcast structures, and strong quantum darwinism – a review.Quantum, 5:571, November 2021. ISSN 2521-327X. doi:10.22331/q-2021-11-08-571. URL http://dx.doi.org/10.22331/q-2021-11-08-571

    work page doi:10.22331/q-2021-11-08-571 2021

  51. [51]

    Quantum darwinism.Nature Physics, 5(3):181–188, March 2009

    Wojciech Hubert Zurek. Quantum darwinism.Nature Physics, 5(3):181–188, March 2009. ISSN 1745-2481. doi:10.1038/nphys1202. URLhttp://dx.doi.org/10. 1038/nphys1202

    work page doi:10.1038/nphys1202 2009

  52. [52]

    Contextual advantages and certification for maximum-confidence discrimination.PRX Quantum, 3:030337, Sep 2022

    Kieran Flatt, Hanwool Lee, Carles Roch I Carceller, Jonatan Bohr Brask, and Joonwoo Bae. Contextual advantages and certification for maximum-confidence discrimination.PRX Quantum, 3:030337, Sep 2022. doi:10.1103/PRXQuantum.3.030337. URLhttps:// link.aps.org/doi/10.1103/PRXQuantum.3.030337

    doi:10.1103/prxquantum.3.030337 2022

  53. [53]

    Unifying contextual advantages in state discrimination, 2025

    Kieran Flatt and Joonwoo Bae. Unifying contextual advantages in state discrimination, 2025. URLhttps: //arxiv.org/abs/2511.04100

    Pith/arXiv arXiv 2025

  54. [54]

    Generalized probabilistic theories without the no-restriction hypothesis.Physical Review A, 87(5), May 2013

    Peter Janotta and Raymond Lal. Generalized probabilistic theories without the no-restriction hypothesis.Physical Review A, 87(5), May 2013. ISSN 1094-1622. doi:10.1103/physreva.87.052131. URL http://dx.doi.org/10.1103/PhysRevA.87.052131. Appendix A: Proofs and More Specific Bounds

    work page doi:10.1103/physreva.87.052131 2013

  55. [55]

    Preparation contextuality as an essential feature underlying quantum communication advantage.Physical Review A, 100(2), August 2019

    Debashis Saha and Anubhav Chaturvedi. Preparation contextuality as an essential feature underlying quantum communication advantage.Physical Review A, 100(2), August 2019. ISSN 2469-9934. doi:10.1103/physreva.100.022108. URLhttp: //dx.doi.org/10.1103/PhysRevA.100.022108

    doi:10.1103/physreva.100.022108 2019

  56. [59]

    Proofs of Theorem 1 and Corollary 1 We will start by proving some useful Lemmas, using the notation ¯λ:= min k[B(ek, sk)] andp min := mink[pk], where{(p k, sk)}is a given SD task ande k denotes the optimal measurement effect for that task. Moreover, we denote byV({q k},{p k}) the total variation distance between probability distributions{q k}and{p k}: V({...

  57. [60]

    F urther bounds: uniform priors and non-extremal states In this appendix we state and prove two refinements of Theorem 1 used in the main text: a bound for uniform priors and a strengthening for sets containing non-extremal states. A case that is often of interest in SD tasks is the one in which the prior is uniform, for which the bound takes a form that ...

  58. [61]

    Then, P k qksk is a linearly independent decomposition for¯sif and only ifP qkL(sk)is a linearly independent decomposition for L(¯s)

    Proof of Corollary 2: Invariance of the geometric SD bounds Lemma 5(Injective linear maps preserve linearly independent decompositions).Consider an ensemble of GPT states{(p k, sk)}k∈K and letL: Span[{s k}k∈K ]→ Wbe an injective linear map. Then, P k qksk is a linearly independent decomposition for¯sif and only ifP qkL(sk)is a linearly independent decompo...

  59. [62]

    First, we recall the notion of a strictly classical GPT system (following Ref

    Proof of Lemma 1 In order to prove Lemma 1, we first introduce three important ingredients. First, we recall the notion of a strictly classical GPT system (following Ref. [28], which are simplicial GPT systems. Definition 1(Simplicial GPT system = strictly classical GPT systems).A simplicial GPT system is a system Gd cl = (∆ n,∆ ∗ n, pΛ)in which the norma...

  60. [63]

    , xn) andx i ∈ {0,

    Proof of Corollary 3 Corollary 3(HighP OC succ implies a classical sub-ensemble).Let{s x}, withx= (x 1, . . . , xn) andx i ∈ {0, . . . , d−1}, be the set of states used in a d-ary oblivious multiplexing task. If this set provides nonclassical advantage in such cases, then for all SD tasks using all states in{s x}, it holds that Pguess <1− 1 dn dn −D dn −D...

  61. [1967]

    doi:10.1016/S0019-9958(67)90530-2

    work page doi:10.1016/s0019-9958(67)90530-2

  62. [2010]

    doi:10.1103/physreva.81.062304

    ISSN 1094-1622. doi:10.1103/physreva.81.062304. 11 URLhttp://dx.doi.org/10.1103/PhysRevA.81. 062304

    work page doi:10.1103/physreva.81.062304

  63. [2025]

    URLhttps://link.aps

    doi:10.1103/f68k-cjx4. URLhttps://link.aps. org/doi/10.1103/f68k-cjx4

    work page doi:10.1103/f68k-cjx4

This paper was first reviewed by deepseek-v4-flash on August 1, 2026.