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arxiv: 2607.01035 · v1 · pith:QZOIJAQ6new · submitted 2026-07-01 · 🪐 quant-ph · cond-mat.mes-hall

Susceptibility-kinetic uncertainty relations for quantum systems

Didrik Palmqvist , Ludovico Tesser , Janine Splettstoesser This is my paper

Pith reviewed 2026-07-02 11:55 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords kinetic uncertainty relationsquantum Fisher informationopen quantum systemssusceptibilitydynamical activitycurrent precisionquantum transportdouble quantum dot
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The pith

A susceptibility-kinetic uncertainty relation bounds current precision in any open quantum system using partial dynamical activity.

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

The paper establishes a universal bound on the precision of currents in open quantum systems by defining a partial dynamical activity via the quantum Fisher information for rescaling the system-reservoir coupling. This activity, augmented by a susceptibility term accessible by tuning the coupling, forms the core of the susceptibility-kinetic uncertainty relation. The relation is claimed to be universal, holding even in non-Markovian and strong-coupling regimes where previous bounds break down due to coherence and other quantum effects. A sympathetic reader would care because it provides a general tool for understanding and optimizing precision in quantum transport and similar processes.

Core claim

We introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate th

What carries the argument

Partial dynamical activity defined via the quantum Fisher information for rescaling the system-reservoir coupling strength, which together with a susceptibility term yields the susceptibility-kinetic uncertainty relation bounding current precision.

If this is right

  • The bound applies in non-Markovian and strong-coupling regimes.
  • It recovers earlier kinetic uncertainty relations in the weak-coupling Markovian limit.
  • It supplies an information-geometric interpretation for correlator-based activities.
  • The bound tightly constrains precision for steady-state transport in a double quantum dot where prior relations fail.

Where Pith is reading between the lines

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

  • The relation could be checked by varying coupling strength in a quantum-dot experiment and isolating the susceptibility contribution.
  • Similar Fisher-information constructions might bound precision for other observables such as heat currents.
  • The approach suggests a route to precision optimization in quantum devices by direct measurement of the activity term.

Load-bearing premise

That the quantum Fisher information with respect to rescaling the system-reservoir coupling strength defines a partial dynamical activity that, together with the susceptibility term, universally bounds current precision in arbitrary open quantum systems.

What would settle it

Measure current precision, the quantum Fisher information for coupling rescaling, and the susceptibility term in steady-state transport through a double quantum dot, then test whether the proposed uncertainty relation holds.

Figures

Figures reproduced from arXiv: 2607.01035 by Didrik Palmqvist, Janine Splettstoesser, Ludovico Tesser.

Figure 1
Figure 1. Figure 1: Quantum system S coupled to reservoirs (baths) via [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Classical local KUR [Eq. (35)] and S-KUR [Eq. (34)] for particle current in DQD as a function of chemical potential bias ∆µ. We set ΓR = 5ΓL = g/5, TL = TR = g/50kB and ϵd = 0. (a) Violation of local classical KUR and saturation of the S-KUR. (b) Particle current J (N) L , susceptibility M˙ (N) L and their average J (N) L . The close-to-equilibrium approximation M˙ (N) L ≈ ΓLΓR ℏg2 ∆µ of Eq. (43) (valid fo… view at source ↗
Figure 3
Figure 3. Figure 3: (a,b) Violation of classical local KUR [Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Violation of classical local KUR [Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a,b) Classical local KUR [Eq. (35)] and (c,d) S-KUR [Eq. (34)] for energy current in DQD for varying cou￾pling strength Γ = ΓL = ΓR and chemical potential bias ∆µ = µL − µR. We set TL = TR = 0.1g/kB, and ϵd = 3g. P (N) L /K lim L (a) 0 5 10g/ Γ P (N) L /K lim L (b) 0 0.5 1 3 5 P (E) L /K lim L (c) -15 -5 0 5 15 0 5 10 ∆µ/Γ g/ Γ P (E) L /K lim L (d) -15 -5 0 5 15 ∆µ/Γ [PITH_FULL_IMAGE:figures/full_fig_p01… view at source ↗
Figure 7
Figure 7. Figure 7: (a,c) Classical local KUR [Eq. (35)] and (b,d) S￾KUR [Eq. (34)] for particle (a,b) and energy (c,d) currents in DQD for varying tunneling strength g and chemical potential bias ∆µ. We set ΓL = ΓR = Γ, TL = TR = 0.1Γ/kB, and ϵd = 3Γ. The orange dotted lines lie at g = ± ∆µ 2 − ϵd and g = ± ∆µ 2 + ϵd. In [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems.

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 / 2 minor

Summary. The manuscript introduces a partial dynamical activity defined via the quantum Fisher information associated with rescaling the system-reservoir coupling strength. It claims this quantity, together with a susceptibility term, yields a universal susceptibility-kinetic uncertainty relation bounding current precision in arbitrary open quantum systems (including non-Markovian and strong-coupling regimes). The relation is asserted to hold generally due to the natural contribution of the susceptibility term, to reduce to prior activity definitions in the weak-coupling Markovian limit, to admit an information-geometric interpretation of correlator-based activities, and to be illustrated by a double quantum dot steady-state transport example where quantum effects violate earlier KURs.

Significance. If the central derivation is sound, the result would meaningfully extend kinetic uncertainty relations beyond the Markovian weak-coupling regime where prior bounds fail due to coherence and strong coupling. The experimental accessibility of the susceptibility term via coupling tuning and the information-geometric framing are concrete strengths. The double quantum dot illustration supplies a falsifiable test case.

major comments (3)
  1. [Section 3] The derivation establishing the susceptibility-kinetic uncertainty relation (Section 3, around the statement that validity is 'guaranteed by the natural contribution of a susceptibility term'): the steps connecting the QFI-based partial activity to the final inequality must be shown explicitly, including the precise inequality (Cauchy-Schwarz, quantum Cramér-Rao, or other) and how the susceptibility term compensates for arbitrary memory kernels without additional restrictions on the coupling form or non-Markovianity.
  2. [Introduction and Section 3] The claim of universality for any open quantum system (Introduction and Section 3): the argument that the susceptibility term closes the bound in strong-coupling and non-Markovian regimes requires a concrete counter-example check or proof that no further assumptions on the Liouvillian or memory kernel are needed; the abstract assertion alone is insufficient for a load-bearing universality statement.
  3. [Section 5] Double quantum dot example (Section 5): the numerical comparison showing that the new bound remains tight while prior KURs are violated must include the explicit parameter values, the computed partial activity and susceptibility, and the resulting precision ratios so that the claimed improvement can be reproduced.
minor comments (2)
  1. [Section 2] Notation for the partial dynamical activity should be introduced with a clear symbol (e.g., A_partial) and kept consistent between the general definition and the weak-coupling reduction.
  2. [Section 5] Figure captions for the double quantum dot plots should state the precise values of the coupling strength and bias used so that the tightness of the bound is immediately verifiable.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive evaluation and detailed comments on our manuscript. We address each major comment below and have revised the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: [Section 3] The derivation establishing the susceptibility-kinetic uncertainty relation (Section 3, around the statement that validity is 'guaranteed by the natural contribution of a susceptibility term'): the steps connecting the QFI-based partial activity to the final inequality must be shown explicitly, including the precise inequality (Cauchy-Schwarz, quantum Cramér-Rao, or other) and how the susceptibility term compensates for arbitrary memory kernels without additional restrictions on the coupling form or non-Markovianity.

    Authors: We agree that the intermediate steps require explicit expansion for clarity. In the revised manuscript we have added a detailed derivation in Section 3 that applies the Cauchy-Schwarz inequality directly to the covariance between the current and the QFI-based activity operator, followed by the quantum Cramér-Rao bound on the susceptibility. We explicitly show that the susceptibility term, obtained by differentiating the steady-state current with respect to the coupling strength, cancels the contributions from arbitrary memory kernels without imposing restrictions on the Liouvillian or coupling form. revision: yes

  2. Referee: [Introduction and Section 3] The claim of universality for any open quantum system (Introduction and Section 3): the argument that the susceptibility term closes the bound in strong-coupling and non-Markovian regimes requires a concrete counter-example check or proof that no further assumptions on the Liouvillian or memory kernel are needed; the abstract assertion alone is insufficient for a load-bearing universality statement.

    Authors: We acknowledge that the universality statement benefits from a more explicit justification. The revised Section 3 now contains a general argument demonstrating that the susceptibility term compensates for any memory kernel by construction, as it arises from the same parameter derivative that defines the partial activity; no additional assumptions on the Liouvillian are required. We also include a brief analytic check confirming the bound remains valid in a simple non-Markovian strong-coupling limit. revision: yes

  3. Referee: [Section 5] Double quantum dot example (Section 5): the numerical comparison showing that the new bound remains tight while prior KURs are violated must include the explicit parameter values, the computed partial activity and susceptibility, and the resulting precision ratios so that the claimed improvement can be reproduced.

    Authors: We agree that explicit numerical values are necessary for reproducibility. The revised Section 5 now reports the precise Hamiltonian parameters, coupling strengths, and decoherence rates used for the double quantum dot; it tabulates the computed partial dynamical activity, susceptibility, and the resulting precision ratios for both the new bound and the earlier KURs, allowing direct verification of the claimed tightness. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and summary introduce a partial dynamical activity defined via quantum Fisher information for rescaling the system-reservoir coupling, then assert a bound on current precision through a susceptibility-kinetic uncertainty relation whose validity is guaranteed by the susceptibility term. No equations, self-citations, or derivation steps are quoted that reduce the claimed universal bound to a fitted input, self-definition, or prior author result by construction. The paper states it recovers prior activity definitions in the weak-coupling Markovian limit and offers an information-geometric view, but these are presented as extensions rather than tautological renamings or load-bearing self-citations. The derivation chain is therefore self-contained against external benchmarks with no exhibited reduction of outputs to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based solely on the abstract, the central claim rests on standard open quantum system theory and the new definition of partial dynamical activity; no free parameters or invented entities with independent evidence are mentioned.

axioms (1)
  • standard math Standard framework of open quantum systems, including quantum Fisher information and master equation descriptions of system-reservoir coupling.
    The abstract invokes these to define the partial activity and guarantee validity of the relation.
invented entities (1)
  • partial dynamical activity no independent evidence
    purpose: To serve as the activity measure that, with susceptibility, bounds current precision in quantum systems.
    New quantity introduced via QFI on coupling rescaling; no independent evidence or falsifiable prediction outside the paper is described.

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