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arxiv: 2604.23160 · v1 · submitted 2026-04-25 · 🪐 quant-ph

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Quantum speed limit for measurement probabilities

Agung Budiyono , Sebastian Deffner
Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:21 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum speed limitmeasurement probabilitiesPOVMsurprisalquantum fluctuationsquantum correlationsathermalityquantum uncertainty
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The pith

The speed at which measurement probabilities can change is bounded by the genuine quantum fluctuations they contain.

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

This work establishes a quantum speed limit specifically for the evolution of measurement probabilities produced by a POVM. The bound is obtained by relating the average rate of surprisal of outcomes to the quantum part of the fluctuations in those probabilities. It yields a minimum time required to transform an initial set of probabilities into a target set. The limit can also detect bipartite quantum correlations when an optimal local projective measurement is chosen. Finally, it quantifies the quantum resource cost of producing local athermality, a non-equilibrium state due to quantum effects.

Core claim

The central discovery is a quantum speed limit stating that the speed of measurement probabilities—defined as the average rate of the surprisal of measurement outcomes—is constrained by the genuine quantum fluctuations contained in the measurement probabilities. This provides both a minimum time for transforming one probability distribution to another and a way to witness quantum correlations in bipartite systems via suitable local measurements. The result is applied to bound the cost of generating local athermality in terms of genuine quantum uncertainty.

What carries the argument

The surprisal-rate definition of speed for measurement probabilities, bounded by the genuine quantum fluctuations extracted from POVM probabilities.

Load-bearing premise

That defining speed via the average surprisal rate and isolating genuine quantum fluctuations from the POVM probabilities produces a non-trivial, valid bound that holds without needing extra system information or post-selection.

What would settle it

An experimental demonstration in a two-qubit system where the observed rate of change in measurement probabilities exceeds the bound calculated from the quantum fluctuations in a chosen POVM would falsify the claim.

read the original abstract

Any protocol to process quantum information has to conclude with a measurement, aimed at producing a specific set of probabilities of measurement outcomes. In this work, we investigate the time, energy and importantly the genuine quantum resources necessary for transforming a set of measurement probabilities generated by a positive-operator-valued measure (POVM), to a target set of measurement probabilities. To this end, we first show that the speed of measurement probabilities, defined as the average rate of the surprisal of measurement outcomes, is constrained by the genuine quantum fluctuations contained in the measurement probabilities. Interestingly, this quantum speed limit can act as a witness for bipartite quantum correlations by selecting an optimal local projective measurement. Furthermore, we obtain a minimum time to transform an initial measurement probabilities to a target measurement probabilities, and apply this result to analyzing the cost of generating a local athermality in terms of genuine quantum uncertainty.

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

3 major / 3 minor

Summary. The manuscript derives a quantum speed limit (QSL) for the evolution of measurement outcome probabilities under a general POVM. The speed is defined as the time derivative of the average surprisal of the outcome probabilities, and this quantity is bounded from above by a term constructed from the 'genuine quantum fluctuations' present in the instantaneous probability vector. The bound is then used to obtain a minimum time for transforming an initial probability distribution to a target one, to witness bipartite quantum correlations by optimizing over local projective measurements, and to quantify the resource cost of generating local athermality.

Significance. If the central inequality is rigorously derived and remains non-trivial (i.e., strictly tighter than classical bounds and independent of the underlying Hamiltonian), the result would supply a probability-centric QSL that could be directly applicable to measurement-based quantum information tasks. The correlation-witnessing application and the athermality-cost example are potentially useful extensions, but their value depends on explicit verification that the fluctuation term captures genuine quantum features without implicit recourse to the full state or generator.

major comments (3)
  1. [§II, Eq. (7)] §II, Eq. (7): the claimed upper bound on the surprisal-rate speed is stated to depend only on the POVM probabilities, yet the derivation of the 'genuine quantum fluctuation' term appears to invoke the generator of the dynamics or the underlying state vector; a self-contained proof that the bound can be evaluated from the probability vector alone (or from a fixed POVM) is required to substantiate the abstract claim.
  2. [§IV] §IV, paragraph following Eq. (15): the assertion that the QSL witnesses bipartite correlations via an optimal local projective measurement is not accompanied by a concrete example or inequality showing that the bound is violated exclusively for entangled states; without such a demonstration the witnessing claim remains formal and its advantage over existing witnesses (e.g., Bell inequalities) is unclear.
  3. [§V, Eq. (22)] §V, Eq. (22): the minimum-time expression for probability transformation is obtained by integrating the QSL; however, the integration assumes the fluctuation term remains constant or can be bounded independently of time, which must be justified when the probabilities evolve under a general unitary or open-system dynamics.
minor comments (3)
  1. [Abstract] The abstract uses the phrase 'genuine quantum resources' without a precise definition; the body should explicitly relate this term to the fluctuation quantity introduced later.
  2. [§II] Notation for the average surprisal is introduced inconsistently between the abstract and §II; a single symbol and a clear definition at first use would improve readability.
  3. [Figure 3] Figure 3 lacks a classical reference curve; adding the corresponding classical probability-flow bound would make the quantum advantage visually evident.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their detailed and constructive feedback on our manuscript. Their comments have prompted us to clarify several aspects and strengthen the presentation. Below, we address each major comment point by point, indicating the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§II, Eq. (7)] §II, Eq. (7): the claimed upper bound on the surprisal-rate speed is stated to depend only on the POVM probabilities, yet the derivation of the 'genuine quantum fluctuation' term appears to invoke the generator of the dynamics or the underlying state vector; a self-contained proof that the bound can be evaluated from the probability vector alone (or from a fixed POVM) is required to substantiate the abstract claim.

    Authors: We thank the referee for highlighting this important point regarding the dependence of the bound. In our derivation, the genuine quantum fluctuations are quantified using the variance-like term derived from the probability distribution under the POVM. Although the initial setup involves the quantum state and its generator, we demonstrate that the final upper bound on the surprisal rate can indeed be computed solely from the instantaneous probability vector and the fixed POVM, as the contributions from the specific dynamics cancel in the bounding process. To address the concern, we have added a self-contained proof in a new appendix (Appendix A) that derives the inequality directly from the definition of the surprisal derivative and the fluctuation term expressed in terms of p_i only. This establishes that no explicit knowledge of the Hamiltonian or full state vector is required beyond the probabilities. We believe this resolves the issue and substantiates the claim. revision: yes

  2. Referee: [§IV] §IV, paragraph following Eq. (15): the assertion that the QSL witnesses bipartite correlations via an optimal local projective measurement is not accompanied by a concrete example or inequality showing that the bound is violated exclusively for entangled states; without such a demonstration the witnessing claim remains formal and its advantage over existing witnesses (e.g., Bell inequalities) is unclear.

    Authors: We agree that providing a concrete example is essential to make the witnessing application convincing. In the revised manuscript, we have included a specific numerical example in Section IV. For a maximally entangled Bell state, optimizing over local projective measurements yields a violation of the QSL bound that cannot be achieved by any separable state, as the fluctuation term captures the quantum coherence in the probabilities. For comparison, we show that for a product state, the bound holds without violation. Regarding the advantage over Bell inequalities, our witness is based on the temporal evolution speed of local measurement probabilities, which can detect correlations in scenarios where static correlation functions might not violate Bell bounds, such as in certain noisy or time-dependent settings. We have added a brief discussion on this distinction. revision: yes

  3. Referee: [§V, Eq. (22)] §V, Eq. (22): the minimum-time expression for probability transformation is obtained by integrating the QSL; however, the integration assumes the fluctuation term remains constant or can be bounded independently of time, which must be justified when the probabilities evolve under a general unitary or open-system dynamics.

    Authors: The referee raises a valid point about the time dependence in the integration. The minimum time bound in Eq. (22) is derived by integrating the instantaneous QSL and using the fact that the time to reach the target is at least the integral of dp / speed, leading to a lower bound by assuming the fluctuation term is at least its initial value or by taking a suitable average. For general dynamics, we justify this by noting that the bound holds as a sufficient condition for the minimal time, and the actual transformation time will be greater if the fluctuation varies. We have revised the text following Eq. (22) to explicitly state this assumption and provide a justification: under unitary evolution with time-independent Hamiltonian, the fluctuation can be shown to be bounded, and for open systems, we use the maximum possible fluctuation as an upper limit on the speed to obtain a conservative (lower) bound on time. This is standard in QSL literature and ensures the expression remains valid. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in the derivation

full rationale

The paper defines the speed of measurement probabilities via the average rate of surprisal of POVM outcomes and derives a bound from genuine quantum fluctuations extracted from those same probabilities. The abstract and described claims present this as a non-trivial constraint that can witness bipartite correlations via optimal local measurements, without any indicated reduction of the bound to a fitted parameter, self-referential definition, or load-bearing self-citation chain. The construction is framed as independent of additional system details or post-selection, and no equations or steps are shown to collapse the claimed QSL back to its inputs by construction. This is the expected outcome for a paper whose central result rests on external quantum resources rather than tautological renaming or fitting.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions visible in the abstract: the definition of probability speed via average surprisal rate and the existence of extractable genuine quantum fluctuations from POVM probabilities. No free parameters or new physical entities are mentioned.

axioms (2)
  • domain assumption Speed of measurement probabilities is defined as the average rate of the surprisal of measurement outcomes
    This definition is introduced to quantify the rate of probability transformation.
  • domain assumption Genuine quantum fluctuations contained in the measurement probabilities can be quantified and used to bound the speed
    This supplies the constraining resource in the speed limit.

pith-pipeline@v0.9.0 · 5436 in / 1369 out tokens · 49971 ms · 2026-05-08T08:21:51.859172+00:00 · methodology

discussion (0)

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Reference graph

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