Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.28892 · Physical review. B./Physical review. B

Reply to “Comment on ‘Scaling and universality at noisy quench dynamical quantum phase transitions’ ”

S. Ansari, Rouhollah Jafari, A. Akbari, M. Abdi

Published Aug 26, 2026• 0 citations
arXivHTMLPDF

Abstract

The Comment by Sirker [] 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, ; Jafari, Akbari, Biderang, and Sirker, ]. Our article [Ansari, Jafari, Akbari, and Abdi, ] 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, ], 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, ].

DOI
10.1103/j7bd-hl5g

Related papers

Comment on: "Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions"

J. Sirker

In Ref. [1], dynamical quantum phase transitions (DQPTs) -- non-analyticities in the Loschmidt return rate at critical times -- are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. The protocol used approximates the noise-averaged mixed state, obtained using a master equation, by a pure state, characterized by its excitation probability. In this comment we rigorously show that: (1) This approximation is exponentially poor in the thermodynamic limit. (2) When using the correct metric, the Loschmidt echo of two density matrices in any two-dimensional Hilbert space can become zero if and only if {\it both} density matrices are pure, ruling out DQPTs for non-zero noise. (3) An a posteriori reinterpretation of the results as an interferometric protocol is possible but such a protocol is unsuitable to investigate the effects of noise on DQPTs because it is inherently blind to decoherence. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.

cond-mat.stat-mechCross-listedarXiv:2511.16509•Physical review. B./Physical review. B•Nov 21, 2025•1 citation

Mixed state dynamical quantum phase transitions

Utso Bhattacharya, Souvik Kumar Bandyopadhyay, Amit Dutta

Preparing an integrable system in a mixed state described by a thermal density matrix, we subject it to a sudden quench and explore the subsequent unitary dynamics. To address the question of whether the nonanalyticities, namely, the dynamical quantum phase transitions (DQPTs), persist when the initial state is mixed, we consider two versions of the generalized Loschmidt overlap amplitude (GLOA). Our study shows that the GLOA constructed using the Uhlmann approach does not show any signature of DQPTs at any nonzero initial temperature. On the other hand, a GLOA defined in the interferometric phase approach through the purifications of the time-evolved density matrix, indeed shows that nonanalyiticies in the corresponding ``dynamical free-energy density'' persist, thereby establishing the existence of mixed state dynamical quantum phase transitions (MSDQPTs). Our work provides a framework that perfectly reproduces both the nonanalyticities and also the emergent topological structure in the pure state limit. These claims are corroborated by analyzing the nonequilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.

arXiv:1705.04555•Physical review. B./Physical review. B•Nov 21, 2017•119 citations

Signature of a nonequilibrium quantum phase transition in the long-time average of the Loschmidt echo

Bozhen Zhou, Chao Yang, Shu Chen

We unveil the role of the long-time average of the Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long-time average of the Loschmidt echo. The nonanalytic behaviors are illustrated by a sharp change in the long-time average of the Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of the rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of the rate function and fidelity susceptibility is also discussed.

arXiv:1908.11572•Physical review. B./Physical review. B•Nov 27, 2019•30 citations

Anatomy of non-Hermitian dynamical quantum phase transitions

Yongxu Fu, Gao Xianlong

We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems that encompasses both biorthogonal and self-norm nonbiorthogonal formulations for pure and mixed states under quantum quench protocols. Our framework provides explicit expressions for the Loschmidt amplitude, Loschmidt echo, and rate function, revealing a universal geometric signature of DQPTs in the two-band model: orthogonality of two related vectors in two-dimensional real space. Strikingly, we demonstrate that nonbiorthogonal quenches from non-Hermitian to Hermitian Hamiltonians under chiral symmetry exhibit emergent topological characteristics of DQPTs, unveiling their fundamental features beyond conventional Hermitian regimes. This work establishes fundamental geometric and topological principles governing quantum criticality in open systems, with implications for quantum sensing and many-body physics in dissipative environments.

arXiv:2507.15384•Physical review. B./Physical review. B•Oct 2, 2025•2 citations

Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems

Takato Yoshimura, Lucas Sá

We study the dynamics of Loschmidt echoes in noisy quantum many-body systems without conservation laws. We first show that the operator Loschmidt echo in noisy unitary dynamics is equivalent to the operator norm of the corresponding dissipative dynamics upon noise averaging. We then analyze this quantity in two complementary ways, revealing universal dynamical behavior. First, we develop a heuristic picture for generic Floquet systems that connects Loschmidt echoes, out-of-time-order correlators, and operator growth, which is valid at any dissipation strength. We assert that the Loschmidt echo has two dynamical regimes depending on the time t and the strength of the noise p : Gaussian decay for p t ≪ 1 and exponential decay (with a noise-independent decay rate) for p t ≫ 1 . Lastly, we rigorously prove all our results for a solvable chaotic many-body quantum circuit, the dissipative random phase model—thus providing exact insight into dissipative quantum chaos.

arXiv:2509.01585•Physical review. B./Physical review. B•Feb 25, 2026•1 citation

Scaling and universality at noisy quench dynamical quantum phase transitions

Saeid Ansari, Rouhollah Jafari, Alireza Akbari +1 more

Dynamical quantum phase transitions (DQPTs) have been studied in the extended X Y model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field X Y model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.

arXiv:2506.14355•Physical review. B./Physical review. B•Jul 15, 2025•7 citations
The Comment by Sirker [] 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, ; Jafari, Akbari, Biderang, and Sirker, ]. Our article [Ansari, Jafari, Akbari, and Abdi, ] 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, ], 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, ].
In Ref. [1], dynamical quantum phase transitions (DQPTs) -- non-analyticities in the Loschmidt return rate at critical times -- are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. The protocol used approximates the noise-averaged mixed state, obtained using a master equation, by a pure state, characterized by its excitation probability. In this comment we rigorously show that: (1) This approximation is exponentially poor in the thermodynamic limit. (2) When using the correct metric, the Loschmidt echo of two density matrices in any two-dimensional Hilbert space can become zero if and only if {\it both} density matrices are pure, ruling out DQPTs for non-zero noise. (3) An a posteriori reinterpretation of the results as an interferometric protocol is possible but such a protocol is unsuitable to investigate the effects of noise on DQPTs because it is inherently blind to decoherence. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.
Preparing an integrable system in a mixed state described by a thermal density matrix, we subject it to a sudden quench and explore the subsequent unitary dynamics. To address the question of whether the nonanalyticities, namely, the dynamical quantum phase transitions (DQPTs), persist when the initial state is mixed, we consider two versions of the generalized Loschmidt overlap amplitude (GLOA). Our study shows that the GLOA constructed using the Uhlmann approach does not show any signature of DQPTs at any nonzero initial temperature. On the other hand, a GLOA defined in the interferometric phase approach through the purifications of the time-evolved density matrix, indeed shows that nonanalyiticies in the corresponding ``dynamical free-energy density'' persist, thereby establishing the existence of mixed state dynamical quantum phase transitions (MSDQPTs). Our work provides a framework that perfectly reproduces both the nonanalyticities and also the emergent topological structure in the pure state limit. These claims are corroborated by analyzing the nonequilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.
We unveil the role of the long-time average of the Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long-time average of the Loschmidt echo. The nonanalytic behaviors are illustrated by a sharp change in the long-time average of the Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of the rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of the rate function and fidelity susceptibility is also discussed.
We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems that encompasses both biorthogonal and self-norm nonbiorthogonal formulations for pure and mixed states under quantum quench protocols. Our framework provides explicit expressions for the Loschmidt amplitude, Loschmidt echo, and rate function, revealing a universal geometric signature of DQPTs in the two-band model: orthogonality of two related vectors in two-dimensional real space. Strikingly, we demonstrate that nonbiorthogonal quenches from non-Hermitian to Hermitian Hamiltonians under chiral symmetry exhibit emergent topological characteristics of DQPTs, unveiling their fundamental features beyond conventional Hermitian regimes. This work establishes fundamental geometric and topological principles governing quantum criticality in open systems, with implications for quantum sensing and many-body physics in dissipative environments.
We study the dynamics of Loschmidt echoes in noisy quantum many-body systems without conservation laws. We first show that the operator Loschmidt echo in noisy unitary dynamics is equivalent to the operator norm of the corresponding dissipative dynamics upon noise averaging. We then analyze this quantity in two complementary ways, revealing universal dynamical behavior. First, we develop a heuristic picture for generic Floquet systems that connects Loschmidt echoes, out-of-time-order correlators, and operator growth, which is valid at any dissipation strength. We assert that the Loschmidt echo has two dynamical regimes depending on the time t and the strength of the noise p : Gaussian decay for p t ≪ 1 and exponential decay (with a noise-independent decay rate) for p t ≫ 1 . Lastly, we rigorously prove all our results for a solvable chaotic many-body quantum circuit, the dissipative random phase model—thus providing exact insight into dissipative quantum chaos.
Dynamical quantum phase transitions (DQPTs) have been studied in the extended X Y model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field X Y model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.