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arxiv: 2606.28892 · v1 · pith:TJC5JGZDnew · submitted 2026-06-27 · ❄️ cond-mat.stat-mech

Reply to Comment on "Scaling and universality at noisy quench dynamical quantum phase transitions"

S. Ansari , R. Jafari , A. Akbari , M. Abdi This is my paper

Pith reviewed 2026-06-30 08:19 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords dynamical quantum phase transitionsnoisy quenchesLoschmidt echoUhlmann-Bures fidelitymixed-state dynamicsoperational protocolreturn rate
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The pith

The reported nonanalyticities in noisy dynamical quantum phase transitions arise from a distinct operational definition of the Loschmidt echo, not the Uhlmann-Bures fidelity.

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

The Comment demonstrates that dynamical quantum phase transitions are absent for nonzero noise when the return rate uses the Uhlmann-Bures fidelity of the noise-averaged density matrix. The original work instead defines the echo via noise-averaged excitation probabilities followed by coherent evolution of a constructed pure state. These two quantities are different physical observables, so the nonanalyticities in one do not conflict with the theorem for the other. Readers should care because the extension of Loschmidt echo to mixed states is not unique and different choices preserve different properties. The reply emphasizes the operational assumption underlying their protocol.

Core claim

There is therefore no direct contradiction between the theorem established for the Uhlmann-Bures return rate and the conclusions obtained for the different operational protocol studied in the original publication. The nonanalyticities concern the two-stage protocol and should not be identified with zeros of the Uhlmann-Bures fidelity.

What carries the argument

The two-stage operational protocol of first computing noise-averaged transition probabilities and then performing coherent pure-state evolution to obtain the logarithm of the Loschmidt echo.

If this is right

  • DQPTs can appear in the operational protocol even with noise.
  • The Uhlmann-Bures theorem applies only to the fidelity-based return rate.
  • Different definitions of mixed-state Loschmidt echo lead to different conclusions about phase transitions.
  • The operational quantity is defined through an explicit assumption about the measurement process.

Where Pith is reading between the lines

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

  • Experimental implementations in quantum simulators might realize the operational protocol through specific preparation and measurement sequences.
  • Comparing the two definitions could reveal which one better captures real noisy dynamics in many-body systems.
  • The distinction highlights the need to specify the physical observable when discussing universality in noisy quenches.

Load-bearing premise

The two quantities—the operational Loschmidt echo from averaged probabilities and the Uhlmann-Bures fidelity of the averaged density matrix—are physically distinct observables.

What would settle it

Direct computation or measurement of both the Uhlmann-Bures return rate and the operational echo for the same noisy quench protocol to check if nonanalyticities persist only in the operational version.

Figures

Figures reproduced from arXiv: 2606.28892 by A. Akbari, M. Abdi, R. Jafari, S. Ansari.

Figure 1
Figure 1. Figure 1: FIG. 1. Adiabatic (solid) and diabatic (dashed) energies for the stan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

The Comment by J. Sirker [arXiv:2511.16509] raises an important issue concerning dynamical quantum phase transitions (DQPTs) in noisy and mixed-state dynamics, namely that the extension of the Loschmidt echo from pure to mixed states is not unique and different extensions preserve different physical properties. The Comment examines a noise-averaged mixed-state fidelity and shows that DQPTs cannot occur for any nonzero noise when the return rate is defined through the Uhlmann-Bures fidelity of the noise-averaged density matrix. This conclusion is valid for the mixed-state fidelity observable discussed in the Comment and is consistent with prior studies [https://doi.org/10.1103/PhysRevB.109.L180303, arXiv:2504.03005]. Our article [https://doi.org/10.1103/mkll-nd46] investigated a different operationally defined quantity: the logarithm of the Loschmidt echo obtained by first determining the noise-averaged excitation probabilities generated during the noisy ramp and then performing a coherent post-ramp evolution of a pure state constructed from these noise-averaged transition probabilities. As emphasized explicitly in our original publication, this observable is defined through an operational assumption and is not the same quantity as the mixed-state fidelity. The nonanalyticities reported in Ref. [https://doi.org/10.1103/mkll-nd46] therefore concern this two-stage operational protocol and should not be identified with zeros of the Uhlmann-Bures fidelity. There is therefore no direct contradiction between the theorem established for the Uhlmann-Bures return rate and the conclusions obtained for the different operational protocol studied in Ref. [https://doi.org/10.1103/mkll-nd46].

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 / 1 minor

Summary. This manuscript is a reply to Comment arXiv:2511.16509 by J. Sirker. It asserts that the nonanalyticities reported in the authors' prior work (doi:10.1103/mkll-nd46) concern a distinct two-stage operational protocol—noise-averaged transition probabilities followed by coherent pure-state evolution—rather than the Uhlmann-Bures fidelity of the noise-averaged density matrix for which the Comment proves the absence of DQPTs at any nonzero noise. The reply concludes there is therefore no direct contradiction between the theorem and the original conclusions.

Significance. If the asserted distinction between observables holds, the reply usefully delimits the scope of the Comment's theorem and preserves the applicability of the original results to their specific operational definition. The manuscript supplies no new derivations or numerical checks but rests on an explicit definitional separation already stated in the cited prior publication.

minor comments (1)
  1. The abstract refers to the original work via the placeholder DOI https://doi.org/10.1103/mkll-nd46; the published reference should be inserted if the manuscript is to appear in final form.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and the recommendation to accept the manuscript. The report accurately summarizes our central point that the nonanalyticities concern a distinct two-stage operational Loschmidt echo rather than the Uhlmann-Bures return rate of the noise-averaged density matrix.

Circularity Check

0 steps flagged

No circularity: definitional clarification without derivation

full rationale

The reply contains no equations, derivations, or predictions. Its central claim—that the original work studied a distinct two-stage operational protocol (noise-averaged transition probabilities followed by coherent pure-state evolution) rather than Uhlmann-Bures fidelity of the noise-averaged density matrix—is presented as a restatement of an explicit definitional distinction already asserted in the cited prior publication by the same authors. No load-bearing step reduces a result to a fit, self-citation theorem, or ansatz by construction; the text simply notes consistency with the comment's theorem applying to a different observable. This is a normal, non-circular clarification of protocol differences.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The reply relies entirely on definitions and distinctions from the original work and the comment; no free parameters, axioms, or invented entities are introduced.

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Reference graph

Works this paper leans on

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    Apply the noisy ramp, solve the master equation, and measure the mode-resolved excitation probabilitiesp k att= 0

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    The return rate in our paper is precisely the interferometric signal generated by this second, fully coherent stage

    Prepare for eachka pure state with noise-averaged pop- 4 ulations(1−pk,pk)and let it evolve coherently under the fixed HamiltonianHf . The return rate in our paper is precisely the interferometric signal generated by this second, fully coherent stage. As noted in the revised Comment, this protocol may be viewed as an interferometric protocol rather than a...

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