Reply to Comment on "Scaling and universality at noisy quench dynamical quantum phase transitions"
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].
Versions
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BibTeX
@misc{ansari2026reply,
title = {{Reply to Comment on "Scaling and universality at noisy quench dynamical quantum phase transitions"}},
author = {S. Ansari and R. Jafari and A. Akbari and M. Abdi},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.28892},
eprint = {2606.28892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reply to Comment on "Scaling and universality at noisy quench dynamical quantum phase transitions"
AU - S. Ansari
AU - R. Jafari
AU - A. Akbari
AU - M. Abdi
PY - 2026
DA - 2026/06/27
PB - arXiv
DO - 10.48550/arxiv.2606.28892
UR - https://arxiv.org/abs/2606.28892
AB - 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].
ER -