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arxiv: 2202.07251 · v2 · submitted 2022-02-15 · 🪐 quant-ph

Uncertainty-disturbance relations and applications

Liang-Liang Sun , Kishor Bharti , Xiang Zhou , Leong-Chuan Kwek , Jingyun Fan , Sixia Yu This is my paper

Pith reviewed 2026-05-24 12:12 UTC · model grok-4.3

classification 🪐 quant-ph
keywords uncertaintydisturbancequantum measurementuncertainty-disturbance relationsvon Neumann entropycoherenceprojective measurementsquantum resources
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The pith

Uncertainty both requires and upper-bounds the intrinsic disturbance caused by quantum measurements.

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

The paper shows that in quantum mechanics, the uncertainty of a measurement outcome is not only a prerequisite for the intrinsic disturbance the measurement produces but also sets an upper limit on that disturbance. This connection is formalized through uncertainty-disturbance relations that hold for general states under rank-one projective measurements. The relations double as uncertainty relations for incompatible observables and supply a practical method to estimate von Neumann entropy, purity, coherence, and genuine randomness from disturbance data. The result unifies two previously separate concepts and supplies a single framework for detecting several quantum resources.

Core claim

Uncertainty serves as a prerequisite for intrinsic disturbance and bounds it from above. The authors formalize the connection through uncertainty-disturbance relations (UDRs) that hold for general states and rank-one projective measurements. For such measurements the UDRs function directly as uncertainty relations that bound the uncertainties of incompatible observables. The same relations permit experimental estimation of von Neumann entropy, purity, coherence, and genuine randomness, thereby unifying the treatment of uncertainty and disturbance while providing a versatile tool for quantum resource detection.

What carries the argument

Uncertainty-disturbance relations (UDRs) that link the uncertainty of a measurement to the intrinsic disturbance it produces and supply explicit upper and lower bounds between them.

If this is right

  • UDRs act as uncertainty relations that bound the uncertainties of incompatible rank-one projective measurements.
  • The relations allow direct experimental estimation of von Neumann entropy from measured disturbance values.
  • Purity, coherence, and genuine randomness become experimentally accessible through the same disturbance measurements.
  • A single set of relations supplies a unified framework for detecting multiple quantum resources.

Where Pith is reading between the lines

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

  • The bounding mechanism may suggest analogous relations for positive-operator-valued measures beyond rank-one projectors.
  • Resource estimation protocols derived from the relations could be tested on current quantum devices by comparing disturbance data against independent entropy or coherence measurements.
  • The unification raises the question whether other pairs of quantum concepts previously treated separately can be linked by similar prerequisite-and-bound structures.

Load-bearing premise

The chosen formal definitions of uncertainty and intrinsic disturbance permit the claimed bounding relations to hold for general states and for rank-one projective measurements.

What would settle it

A concrete counter-example state and rank-one projective measurement pair for which the derived upper bound on disturbance in terms of uncertainty is violated.

Figures

Figures reproduced from arXiv: 2202.07251 by Jingyun Fan, Kishor Bharti, Leong-Chuan Kwek, Liang-Liang Sun, Sixia Yu, Xiang Zhou.

Figure 1
Figure 1. Figure 1: Geometrical visualization of the constraints of un [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them, proving that uncertainty not only serves as a prerequisite for intrinsic disturbance but also bounds it from above. We formalize this connection via uncertainty-disturbance relations (UDRs) with direct applications in quantum information science. We show that for rank-one projective measurements, these UDRs effectively function as uncertainty relations by bounding the uncertainties of incompatible measurements. They also enable the experimental estimation of key quantum resources -- including von Neumann entropy, purity, coherence, and genuine randomness. Our findings thus unify the understanding of uncertainty and disturbance and provide a versatile framework for quantum resource detection.

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 / 3 minor

Summary. The manuscript establishes uncertainty-disturbance relations (UDRs) for quantum measurements. It claims that, under the chosen formal definitions, uncertainty is both a prerequisite for and an upper bound on intrinsic disturbance for general states under rank-one projective measurements. The UDRs are then applied to show that they function as uncertainty relations for incompatible observables and to derive estimators for von Neumann entropy, purity, coherence, and genuine randomness.

Significance. If the derivations from the stated definitions hold without hidden restrictions, the work provides a direct link between two previously separate concepts and yields practical corollaries for resource estimation. The parameter-free character of the bounds (once the definitions are fixed) and the explicit applications to entropy and coherence estimation are strengths that would be of interest to the quantum information community.

minor comments (3)
  1. The abstract states that proofs exist but the introduction and main text should explicitly flag the precise definitions of uncertainty and intrinsic disturbance (e.g., which entropy or variance measure is used) before the first theorem, to allow immediate verification of the claimed scope.
  2. Section 3 (applications) would benefit from a short table comparing the new estimators against existing ones in terms of required measurements or assumptions, to clarify the practical advantage.
  3. A few typographical inconsistencies appear in the notation for the disturbance operator (D vs. D̂) across equations (12)–(15); standardize throughout.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision for our manuscript on uncertainty-disturbance relations. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The central derivations establish UDRs directly from the paper's chosen formal definitions of uncertainty and intrinsic disturbance, applied to general states under rank-one projective measurements. These relations are obtained by algebraic manipulation of the definitions without reducing to fitted parameters, self-citation chains, or ansatzes imported from prior work by the same authors. Applications to entropy, coherence, and randomness follow as direct corollaries once the UDRs are in place. No load-bearing step equates a claimed result to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; ledger left empty pending full text.

pith-pipeline@v0.9.0 · 5661 in / 871 out tokens · 15607 ms · 2026-05-24T12:12:36.683073+00:00 · methodology

discussion (0)

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