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Reply to “Comment on ‘Scaling and universality at noisy quench dynamical quantum phase transitions’ ”
Phys. Rev. B 114, 206302 – Published 5 October, 2026
DOI: https://doi.org/10.1103/j7bd-hl5g
Abstract
The Comment by 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 [Jafari, Langari, Eggert, and Johannesson, Phys. Rev. B 109, L180303 (2024); Jafari, Akbari, Biderang, and Sirker, arXiv:2504.03005]. Our article [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)] 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 postramp 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 [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)], 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 [Ansari, Jafari, Akbari, and Abdi, Phys. Rev. B 112, 054304 (2025)].
Physics Subject Headings (PhySH)
Comments & Replies
Comment on “Scaling and universality at noisy quench dynamical quantum phase transitions”
Article Text
Original Article
Scaling and universality at noisy quench dynamical quantum phase transitions
References (19)
- R. Jafari, A. Langari, S. Eggert, and H. Johannesson, Dynamical quantum phase transitions following a noisy quench, Phys. Rev. B 109, L180303 (2024).
- R. Jafari, A. Akbari, M. Biderang, and J. Sirker, Noise-affected dynamical quantum phase transitions, arXiv:2504.03005.
- S. Ansari, R. Jafari, A. Akbari, and M. Abdi, Scaling and universality at noisy quench dynamical quantum phase transitions, Phys. Rev. B 112, 054304 (2025).
- R. Jafari, J. Naji, A. Langari, V. Karimipour, and H. Johannesson, Entanglement generation and scaling from noisy quenches across a quantum critical point, Phys. Rev. Res. 7, 043087 (2025).
- J. Naji, R. Jafari, A. Akbari, and M. Abdi, Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench, Phys. Rev. B 112, 144312 (2025).
- M.-Z. Ai, J.-M. Cui, R. He, Z.-H. Qian, X.-X. Gao, Y.-F. Huang, C.-F. Li, and G.-C. Guo, Experimental verification of anti–Kibble-Zurek behavior in a quantum system under a noisy control field, Phys. Rev. A 103, 012608 (2021).
- K. Yang, L. Zhou, W. Ma, X. Kong, P. Wang, X. Qin, X. Rong, Y. Wang, F. Shi, J. Gong, and J. Du, Floquet dynamical quantum phase transitions, Phys. Rev. B 100, 085308 (2019).
- W. Ma, L. Zhou, Q. Zhang, M. Li, C. Cheng, J. Geng, X. Rong, F. Shi, J. Gong, and J. Du, Experimental observation of a generalized Thouless pump with a single spin, Phys. Rev. Lett. 120, 120501 (2018).
- B. Chen, X. Hou, F. Zhou, P. Qian, H. Shen, and N. Xu, Detecting the out-of-time-order correlations of dynamical quantum phase transitions in a solid-state quantum simulator, Appl. Phys. Lett. 116, 194002 (2020).
- A. Dutta, A. Rahmani, and A. del Campo, Anti-Kibble-Zurek behavior in crossing the quantum critical point of a thermally isolated system driven by a noisy control field, Phys. Rev. Lett. 117, 080402 (2016).
- S. Sadeghizade, R. Jafari, and A. Langari, Anti-Kibble-Zurek behavior in the quantum XY spin- chain driven by correlated noisy magnetic field and anisotropy, Phys. Rev. B 111, 104310 (2025).
- Z.-P. Gao, D.-W. Zhang, Y. Yu, and S.-L. Zhu, Anti-Kibble-Zurek behavior of a noisy transverse-field chain and its quantum simulation with two-level systems, Phys. Rev. B 95, 224303 (2017).
- N. V. Vitanov, Transition times in the Landau-Zener model, Phys. Rev. A 59, 988 (1999).
- M. Singh and S. Gangadharaiah, Driven quantum spin chain in the presence of noise: Anti-Kibble-Zurek behavior, Phys. Rev. B 104, 064313 (2021).
- S. M. Griffin, M. Lilienblum, K. T. Delaney, Y. Kumagai, M. Fiebig, and N. A. Spaldin, Scaling behavior and beyond equilibrium in the hexagonal manganites, Phys. Rev. X 2, 041022 (2012).
- J. Sirker, Comment on “Scaling and universality at noisy quench dynamical quantum phase transitions”, Phys. Rev. B 114, 206301 (2026).
- R. Jafari and A. Akbari, Scaling and universality at noise-affected nonequilibrium spin correlation functions, Phys. Rev. B 113, L220302 (2026).
- G. Parez and V. Alba, Smearing of dynamical quantum phase transitions in dissipative free-fermion systems, Phys. Rev. B 113, 144310 (2026).
- G. Parez and V. Alba, Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect, J. Stat. Mech.: Theory Exp. (2026) 013103.
