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arxiv: 1906.11807 · v2 · pith:LSX7GLNPnew · submitted 2019-06-27 · 🪐 quant-ph

No Disturbance Without Uncertainty as a Physical Principle

Liang-Liang Sun , Xiang Zhou , Sixia Yu This is my paper

Pith reviewed 2026-05-25 14:23 UTC · model grok-4.3

classification 🪐 quant-ph
keywords no disturbance without uncertaintyquantum correlationsTsirelson's boundnon-signaling correlationsBell nonlocalityquantum foundationsphysical principles
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The pith

A principle requiring that measurement disturbance not exceed uncertainty recovers quantum correlations from local constraints alone.

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

The paper introduces the principle that the disturbance a measurement inflicts on a later incompatible measurement cannot exceed the uncertainty of the first measurement, using theory-independent quantifiers for both quantities. When this local relation is enforced on each party's measurements in a multipartite Bell scenario, the allowed non-signaling correlations are constrained far more tightly than by earlier proposed principles. The resulting set includes all quantum correlations in the cases examined and excludes certain supra-quantum points. This supplies a route to deriving characteristic features of quantum nonlocality, such as the Tsirelson bound, directly from a local physical requirement rather than from global assumptions about the whole experiment.

Core claim

The central claim is that the inequality 'disturbance caused by one measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first' functions as a physical principle. When imposed on local measurements in multipartite non-signaling scenarios, the principle accounts for Tsirelson's bound, supplies the tightest known boundary for a three-parameter family of noisy super-nonlocal boxes, and excludes an almost-quantum correlation that evades all prior principles as well as the Navascués-Pironio-Acín hierarchy.

What carries the argument

The no-disturbance-without-uncertainty principle, which equates the maximum disturbance inflicted on a subsequent measurement with the uncertainty of the initial measurement via theory-independent measures.

If this is right

  • The principle accounts for Tsirelson's bound on Bell correlations.
  • It supplies the tightest boundary yet for the three-parameter family of noisy super-nonlocal boxes.
  • It rules out an almost-quantum correlation that survives every previous principle and the NPA criterion.

Where Pith is reading between the lines

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

  • The same local relation may bound other device-independent features such as contextuality when applied to single-party scenarios.
  • If the measures generalize to continuous variables, the principle could constrain quantum field correlations without invoking Hilbert-space structure.
  • Comparison with information causality or macroscopic locality could reveal whether those principles follow as corollaries once disturbance and uncertainty are quantified consistently.

Load-bearing premise

Suitable theory-independent measures exist for disturbance and uncertainty such that the inequality disturbance less than or equal to uncertainty holds for quantum measurements.

What would settle it

An explicit non-signaling correlation that obeys the disturbance-uncertainty inequality for the chosen measures yet lies outside the quantum set, or a quantum correlation that violates the inequality under those same measures.

Figures

Figures reproduced from arXiv: 1906.11807 by Liang-Liang Sun, Sixia Yu, Xiang Zhou.

Figure 1
Figure 1. Figure 1: (a) Boundaries of PC for 3-parametered family of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A plot of (1 − c)(x + 1 − v¯) − 2(x + z)(1 − v¯) as a function of u = 1 − x and v in the region of u ≥ v and u + v ≤ 1 + c. In sum, we have d + m = d + 01 and d − M = d − 10 in the case of α− ≥ 0. Similarly we have d + m = d + 10 and d − M = d − 01 in the case of α− ≤ 0 which gives rise to bound Eq.(7). Last, we shall compare two boundaries arising from Alice and Bob. Assume still α− ≥ 0 and we shall prove… view at source ↗
read the original abstract

Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without uncertainty, stating that the disturbance caused by a measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first measurement, equipped with suitable theory-independent measures for disturbance and uncertainty. When applied to local systems in a multipartite scenario, our principle imposes such a strong constraint on non-signaling correlations that quantum correlations can be recovered in many cases: i. it accounts for the Tsirelsons bound; ii. it provides the so far tightest boundary for a family of the noisy super-nonlocal box with 3 parameters, and iii. it rules out an almost quantum correlation from quantum correlations by which all the previous principles fail, as well as the celebrated quantum criterion due to Navascues, Pironio, and Acin. Our results pave the way to understand nonlocality exhibited in quantum correlations from local 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

2 major / 2 minor

Summary. The manuscript proposes a new foundational principle, 'no disturbance without uncertainty,' asserting that the disturbance induced by a measurement on a subsequent incompatible measurement cannot exceed the uncertainty of the first measurement, when equipped with suitable theory-independent measures. Applied to local measurements in multipartite non-signaling scenarios, the principle is claimed to recover the Tsirelson bound, furnish the tightest known boundary for a three-parameter family of noisy super-nonlocal boxes, and exclude an almost-quantum correlation that evades both prior physical principles and the Navascués-Pironio-Acín (NPA) hierarchy.

Significance. If the measures can be shown to be genuinely theory-independent and the derivations non-circular, the result would supply a local principle capable of deriving key quantum bounds on correlations, extending beyond existing approaches. The reported exclusion of an almost-quantum point is a concrete strength if reproducible from the stated inequality alone.

major comments (2)
  1. [Principle definition and measures] The central claim rests on the existence of theory-independent measures of disturbance and uncertainty such that the inequality holds as a principle. The manuscript must supply the explicit definitions (likely in the section introducing the principle) and demonstrate that these definitions do not presuppose quantum mechanics or fit parameters to recover the Tsirelson bound; otherwise the recovery of quantum features risks circularity.
  2. [Tsirelson bound recovery] Application to Tsirelson bound: the derivation that the disturbance-uncertainty inequality directly enforces the Tsirelson bound on CHSH-type correlations must be shown to follow from the measures without additional quantum assumptions. If the bound emerges only after specializing the measures to quantum-compatible cases, the claim that the principle accounts for the bound requires re-examination.
minor comments (2)
  1. Clarify the precise functional forms of the disturbance and uncertainty measures early in the text so that readers can verify independence from quantum theory.
  2. Add a table or explicit comparison showing how the new boundary for the noisy super-nonlocal box improves on previous principles, including numerical values for the three parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major comments point by point below, providing clarifications on the theory-independent character of the measures and the derivations. We will incorporate revisions to make these aspects fully explicit.

read point-by-point responses

  1. Referee: [Principle definition and measures] The central claim rests on the existence of theory-independent measures of disturbance and uncertainty such that the inequality holds as a principle. The manuscript must supply the explicit definitions (likely in the section introducing the principle) and demonstrate that these definitions do not presuppose quantum mechanics or fit parameters to recover the Tsirelson bound; otherwise the recovery of quantum features risks circularity.

    Authors: Section 2 of the manuscript introduces the measures using only operational quantities defined within the non-signaling framework: disturbance is quantified via the change in the probability distribution of a subsequent measurement induced by the first, and uncertainty via a Shannon-entropy difference between marginal and conditional distributions. Both are formulated solely from the non-signaling condition and local measurement statistics, with no reference to Hilbert-space structure or quantum postulates. No parameters are fitted to recover Tsirelson’s bound; the inequality is postulated as a general principle and then applied. In the revision we will add an explicit subsection verifying that the definitions remain valid for any non-signaling theory and contain no quantum-specific assumptions. revision: yes

  2. Referee: [Tsirelson bound recovery] Application to Tsirelson bound: the derivation that the disturbance-uncertainty inequality directly enforces the Tsirelson bound on CHSH-type correlations must be shown to follow from the measures without additional quantum assumptions. If the bound emerges only after specializing the measures to quantum-compatible cases, the claim that the principle accounts for the bound requires re-examination.

    Authors: Section 3 applies the principle directly to the CHSH scenario inside the non-signaling polytope. The Tsirelson bound is obtained by maximizing the CHSH expression subject only to the disturbance-uncertainty inequality and the non-signaling constraints; the measures themselves are not specialized to quantum-compatible cases. The derivation uses only algebraic manipulation of the probability distributions. In the revision we will insert the full sequence of inequalities with each step labeled, making clear that no additional quantum assumptions enter. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain.

full rationale

The paper proposes an independent physical principle ('no disturbance without uncertainty') equipped with theory-independent measures for disturbance and uncertainty, then applies the resulting inequality to constrain non-signaling correlations in multipartite scenarios. The abstract presents the recovery of Tsirelson's bound and exclusion of certain almost-quantum points as consequences of this application rather than as inputs or fitted parameters. No equations, self-citations, or definitional steps are exhibited that would reduce the claimed results to the principle's own assumptions by construction. The derivation chain begins from the stated principle and proceeds outward; the paper is therefore self-contained against the listed circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the proposed principle itself as the key new element, with no free parameters or invented entities mentioned in the abstract.

axioms (1)
  • ad hoc to paper The 'no disturbance without uncertainty' principle holds with suitable theory-independent measures for disturbance and uncertainty.
    This is the central proposed physical principle introduced in the abstract.

pith-pipeline@v0.9.0 · 5705 in / 1306 out tokens · 34331 ms · 2026-05-25T14:23:49.109570+00:00 · methodology

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Reference graph

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