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arxiv: 2402.12446 · v2 · submitted 2024-02-19 · 🪐 quant-ph

Theories with no superluminal signaling have greater information-processing power than theories with no superluminal causation

V. Vilasini , Roger Colbeck This is my paper

Pith reviewed 2026-05-24 04:00 UTC · model grok-4.3

classification 🪐 quant-ph
keywords relativistic causalityno superluminal causationno superluminal signalingnon-classical correlationsPR-boxesretrocausalityinformation processingspacetime configuration
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The pith

Theories with no superluminal causation cannot achieve certain correlation tasks that no-superluminal-signaling theories can.

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

The paper distinguishes no superluminal causation from no superluminal signaling as separate relativistic principles. It identifies a spacetime configuration where generating non-classical correlations is impossible for any theory obeying no superluminal causation. However, theories that allow superluminal causation but forbid signaling can complete the task perfectly. This holds even in setups where outcomes precede settings in time, enabling certifiable retrocausality without signaling violations.

Core claim

There exists a spacetime configuration in which the task of generating non-classical correlations cannot be achieved in any theory satisfying no superluminal causation, but theories violating no superluminal causation while satisfying no superluminal signaling can perfectly achieve the task. A protocol is provided for operational certification in general spacetimes, and in (1+1)D Minkowski spacetime the task remains achievable even when measurement outcomes occur arbitrarily earlier than the settings.

What carries the argument

The formal distinction between no superluminal causation (NSC) and no superluminal signaling (NSS) applied to a correlation generation task in a specific spacetime configuration.

Load-bearing premise

The definitions of NSC and NSS as distinct, and the selected spacetime configuration and task, accurately isolate the difference in processing power without extra modeling assumptions.

What would settle it

A concrete counterexample would be any theory satisfying NSC that nonetheless succeeds at the task in the described spacetime configuration.

Figures

Figures reproduced from arXiv: 2402.12446 by Roger Colbeck, V. Vilasini.

Figure 1
Figure 1. Figure 1: FIG. 1. Space-time embeddings for the variables [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The causal structure corresponding to the causal [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by considering various information-theoretic principles. Here, we initiate a similar approach considering relativistic causality principles. No superluminal causation (NSC) and no superluminal signalling (NSS) are distinct relativistic principles, requiring, respectively, that causal influence/the ability of agents to signal are within the future lightcone. After formalizing their distinction, we investigate how well theories constrained by NSC and NSS perform in a task that involves generating non-classical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or post-quantum) satisfying NSC. However, we show that theories violating NSC but satisfying NSS can perfectly achieve the task. We give a protocol that would, in a world allowing superluminal causation, enable its operational certification without violating NSS, in general spacetimes. In the case of $(1+1)$D Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a new form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of non-classical post-quantum resources: PR-boxes and jamming. Our work offers insights into the role of different relativistic causality principles in fundamental physics and paves the way for characterising the information-theoretic structure of theories obeying such principles.

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 formalizes the distinction between no superluminal causation (NSC) and no superluminal signalling (NSS) as relativistic principles. It identifies a spacetime configuration and task for generating non-classical correlations that cannot be achieved in any theory (classical, quantum, or post-quantum) satisfying NSC, but can be perfectly achieved in theories violating NSC while satisfying NSS. It supplies an explicit protocol for operational certification of the task in general spacetimes, including a (1+1)D Minkowski case enabling certifiable retrocausality without NSS violation, and illustrates the separation via PR-boxes and jamming resources.

Significance. If the central separation holds, the result demonstrates that NSS permits strictly greater information-processing power than NSC by enabling an otherwise impossible task. The explicit operational definitions in §2, the impossibility argument for NSC theories, and the constructive protocol in §4 constitute clear strengths, as does the direct derivation of the retrocausality example from the same definitions without additional modeling assumptions.

minor comments (2)
  1. [§2] §2: the operational distinction between NSC and NSS would be easier to track if the definitions were accompanied by a short side-by-side comparison of the allowed causal influences and signalling capabilities.
  2. [§4] §4: the protocol description would benefit from an explicit spacetime diagram (with labeled agent world-lines, measurement events, and light cones) to make the configuration and the retrocausality claim visually immediate.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, recognition of the manuscript's strengths, and recommendation of minor revision. No major comments are provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation is self-contained: section 2 supplies independent operational definitions of NSC and NSS that do not presuppose the target separation; the impossibility result for NSC theories follows directly from those definitions applied to the chosen spacetime configuration and task; the explicit protocol in section 4 realizes the task under NSS without invoking fitted parameters, self-referential equations, or load-bearing self-citations. The (1+1)D retrocausality example is likewise obtained by direct substitution of the same definitions. No step reduces by construction to its inputs, and the central claim therefore rests on logically independent content rather than circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard relativistic background assumptions about light-cone structure and the introduction of a new task to compare the two principles.

axioms (1)
  • standard math Spacetime causal structure is defined by light cones in Minkowski geometry
    Invoked as the setting in which NSC and NSS are formalized.
invented entities (1)
  • The specific task requiring non-classical correlations under chosen spacetime configuration no independent evidence
    purpose: To exhibit the difference in power between NSC and NSS theories
    Introduced by the authors to demonstrate the information-processing distinction.

pith-pipeline@v0.9.0 · 5804 in / 1284 out tokens · 33398 ms · 2026-05-24T04:00:20.218848+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Characterizing Signalling: Connections between Causal Inference and Space-time Geometry

    gr-qc 2024-03 unverdicted novelty 7.0

    Introduces the order-theoretic property of conicality for space-times and proves a correspondence between conical space-times and faithful information-theoretic causal models under no-superluminal-signalling constraints.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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    Wiseman, H. M. & Cavalcanti, E. G. Causarum in- vestigatio and the two Bell’s theorems of John Bell. arXiv:1503.06413 (2015). link. 5 A FURTHER DETAILS OF THE CAUSAL MODELLING FRAMEWORK Appendix A: Further details of the causal modelling framework In the main text, we have provided a rather non- technical overview of the causality framework of [3, 4] whic...

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  12. [12]

    Hence, (Λ ⊥d AC), which implies the conditional independence P (Λ|AC) = P (Λ)

    Since Λ is not embedded in the space-time future of A or C, and A and C have no incoming arrows in the causal model, using NSC it follows that all paths between Λ and AC must contain a collider. Hence, (Λ ⊥d AC), which implies the conditional independence P (Λ|AC) = P (Λ)

    work page

  13. [13]

    There could be a collider where the central variable W is embedded in the future of both X and Z, or a fork where the central variable is embedded in the past of X and Z

    Since X and Z are spacelike separated, NSC means there are no directed paths between X and Z in the causal model. There could be a collider where the central variable W is embedded in the future of both X and Z, or a fork where the central variable is embedded in the past of X and Z. Candidates for the central variable in a fork are Λ or a vari- able unde...

    work page

  14. [14]

    Since C has no incoming ar- rows, all paths between X and C must contain a collider with central variable in the future of C

    Since X and C are spacelike separated, NSC means there are no directed paths between X and C in the causal model. Since C has no incoming ar- rows, all paths between X and C must contain a collider with central variable in the future of C. It follows that ( X ⊥d C|AΛ), and conse- quently P (X|ΛAC) = P (X|ΛA). Symmetrically, we also have (Z ⊥d A|CΛ) and he...

    work page