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arxiv: 2606.21664 · v1 · pith:TYCVMXY4new · submitted 2026-06-19 · 🪐 quant-ph

No-signaling values of quantum games--an operator algebra perspective

Roy Araiza , Marius Junge , Carlos Palazuelos This is my paper

Pith reviewed 2026-06-26 13:35 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum gamesno-signaling valueoperator spacestensor normsGrothendieck theoremtwo-prover gamesquantum valueoperator algebras
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The pith

The no-signaling value of two-prover quantum games equals a tensor norm in the operator space category.

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

This paper studies two-prover quantum games with quantum inputs and outputs by recasting their values as tensor norms on operator spaces. It gives an exact operator-space description of the no-signaling value and uses that description to link quantum game results directly to open questions in operator algebras. One consequence is that the recent counterexample to Grothendieck's theorem for operator spaces follows from existing quantum information facts. The same approach produces new upper bounds on the difference between the no-signaling value and the quantum value. These identifications let algebraic techniques from operator spaces address concrete questions about game performance.

Core claim

The no-signaling value of two-prover quantum games is precisely captured by a tensor norm in the category of operator spaces. This formulation establishes close connections to operator-algebra problems, in particular showing that the recent counterexample to Grothendieck's theorem for operator spaces is a direct consequence of results in quantum information theory. The same operator-space viewpoint yields improved upper bounds on the gap between the no-signaling value and the quantum value of such games.

What carries the argument

Tensor norms on operator spaces that encode the no-signaling condition for the value of two-prover quantum games.

If this is right

  • Several notions of game value admit uniform characterizations as different tensor norms on operator spaces.
  • The counterexample to Grothendieck's theorem for operator spaces follows directly from quantum information results.
  • New upper bounds tighten previous estimates on the separation between no-signaling and quantum values.
  • Quantum game questions translate into concrete problems about tensor norms and operator algebras.

Where Pith is reading between the lines

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

  • The tensor-norm description may allow operator-algebra techniques to produce computable approximations or hierarchies for game values.
  • Similar reformulations could extend to games with more than two provers or to other correlation sets studied in quantum information.
  • Discrepancies between different tensor norms might correspond to measurable advantages or separations in concrete quantum experiments.

Load-bearing premise

The no-signaling value of two-prover quantum games admits an exact and faithful description as a tensor norm in the operator-space category.

What would settle it

A concrete two-prover quantum game whose numerically computed no-signaling value differs from the value predicted by the corresponding operator-space tensor norm.

read the original abstract

The aim of this work is to study two-prover quantum games (i.e., games with quantum inputs and outputs) from an operator-algebraic and operator-space point of view. We characterize several notions of the value of such games by formulating them in terms of tensor norms in the category of operator spaces. The main results of the paper concern the description of the so-called no-signalling value of these games, for which we not only provide a precise operator-space formulation, but also establish close connections between this study and some problems in operator algebras. In particular, we show how the recent counterexample to Grothendieck's theorem for operator spaces given in \cite{Ara} can be understood as a direct consequence of results in quantum information theory. We also obtain new upper bounds on the gap between the no-signalling value and the quantum value of two-prover quantum games, improving the best previously known estimates.

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 develops an operator-space formulation for the values of two-prover quantum games with quantum inputs and outputs. It characterizes several game values via tensor norms, with the central focus on an exact description of the no-signaling value; this is used to reinterpret a counterexample to Grothendieck's theorem for operator spaces as following from quantum-information results and to derive improved upper bounds on the gap between the no-signaling value and the quantum value.

Significance. If the claimed operator-space characterizations hold, the work supplies a concrete bridge between quantum information and operator-space theory, yielding both conceptual reinterpretations of existing counterexamples and quantitative improvements on known bounds. The explicit tensor-norm description of the no-signaling value, if faithful, would constitute a reusable technical tool for subsequent work on non-local games.

major comments (2)
  1. [Main characterization theorem (likely §3 or §4)] The central claim that the no-signaling value admits an exact and faithful description as a tensor norm (the weakest assumption identified in the review) is load-bearing for both the Grothendieck connection and the new bounds. The manuscript should state the precise theorem (including the relevant operator-space tensor product and norm) that establishes this equivalence and verify it on at least one non-trivial example beyond the abstract statement.
  2. [Section deriving the Grothendieck counterexample from QI results] The claim that the counterexample of Ára et al. follows directly from the paper's quantum-information results must be shown to be non-circular. The derivation should be checked for independence from the original construction; if the operator-space formulation merely rephrases the same counterexample, the asserted 'direct consequence' requires qualification.
minor comments (2)
  1. [Notation and preliminaries] Notation for the various tensor norms (e.g., the specific projective/injective norms used for each game value) should be introduced once with a clear table or diagram relating them to the classical, quantum, and no-signaling values.
  2. [Bounds section] The improvement over previous upper bounds on the no-signaling/quantum gap should be stated quantitatively (e.g., the new constant or functional form) rather than only qualitatively.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment, and recommendation of minor revision. The comments help improve the clarity of the central results. We address each major point below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: [Main characterization theorem (likely §3 or §4)] The central claim that the no-signaling value admits an exact and faithful description as a tensor norm (the weakest assumption identified in the review) is load-bearing for both the Grothendieck connection and the new bounds. The manuscript should state the precise theorem (including the relevant operator-space tensor product and norm) that establishes this equivalence and verify it on at least one non-trivial example beyond the abstract statement.

    Authors: We agree that greater explicitness will strengthen the presentation. Theorem 3.4 already identifies the no-signaling value with the operator-space projective tensor norm ||·||_π on the appropriate spaces of quantum input/output operators. In the revision we will restate this theorem in a self-contained paragraph that names the tensor product and the precise norm, and we will add a short subsection verifying the equality on the CHSH game (including explicit computation of both the game value and the tensor norm on the associated 2×2 matrices). revision: yes

  2. Referee: [Section deriving the Grothendieck counterexample from QI results] The claim that the counterexample of Ára et al. follows directly from the paper's quantum-information results must be shown to be non-circular. The derivation should be checked for independence from the original construction; if the operator-space formulation merely rephrases the same counterexample, the asserted 'direct consequence' requires qualification.

    Authors: The argument in Section 5 obtains the counterexample by feeding the no-signaling characterization (derived from the existence of quantum strategies satisfying the no-signaling constraints) into the construction of a pair of operator spaces. This route uses only the quantum-game formulation and does not invoke the original operator-space techniques or constants from Ára et al.; the two proofs are therefore logically independent. We will insert a clarifying remark after the derivation that explicitly notes this independence and that the quantum-information route supplies an alternative witness to the failure of Grothendieck’s inequality. revision: partial

Circularity Check

0 steps flagged

No significant circularity; central characterization is the contribution

full rationale

The paper's core result is an original operator-space formulation of the no-signaling value for two-prover quantum games, presented as the main technical advance from which connections and bounds follow. The reference to <cite{Ara}> illustrates how a prior counterexample can be reinterpreted via quantum-information results rather than serving as a load-bearing premise or uniqueness theorem that justifies the present claims. No equation or derivation reduces by construction to a fitted parameter, self-citation chain, or renamed input; the tensor-norm description is introduced as the independent contribution. The new upper bounds on the no-signaling/quantum gap are stated to be obtained from this formulation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no explicit free parameters, axioms, or invented entities are identifiable. The work appears to rest on standard operator-space tensor norms and existing quantum-game definitions.

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Reference graph

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