SciPost Submission Page
Generalized Loschmidt echo and information scrambling in open systems
by Yi-Neng Zhou and Chang Liu
Submission summary
| Authors (as registered SciPost users): | Yi-Neng Zhou |
| Submission information | |
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| Preprint Link: | scipost_202501_00016v2 (pdf) |
| Date submitted: | Dec. 8, 2025, 4:51 p.m. |
| Submitted by: | Yi-Neng Zhou |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Quantum information scrambling, typically explored in closed quantum systems, describes the spread of initially localized information throughout a system and can be quantified by measures such as the Loschmidt echo (LE) and out-of-time-order correlator (OTOC). In this paper, we explore information scrambling in the presence of dissipation by generalizing the concepts of LE and OTOC to open quantum systems governed by Lindblad dynamics. We investigate the universal dynamics of the generalized LE across regimes of weak and strong dissipation. In the weak dissipation regime, we identify a universal structure, while in the strong dissipation regime, we observe a distinctive two-local-minima structure, which we interpret through an analysis of the Lindblad spectrum. Furthermore, we establish connections between the thermal averages of LE and OTOC and prove a general relation between OTOC and Rényi entropy in open systems. Finally, we propose an experimental protocol for measuring OTOC in open systems. These findings provide deeper insights into information scrambling under dissipation and pave the way for experimental studies in open quantum systems.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We would like to thank you for overseeing the review of our manuscript, and we are grateful to the Referees for their careful reading, constructive criticism, and helpful comments.
We are pleased that Referee A recognizes the importance and timeliness of our work, as well as the clarity and structure of our presentation, and that they view our results as opening a promising new research direction. We also appreciate the referee’s valuable comments regarding the generality of some of our claims and the need to clarify the assumptions underlying our analytical relations. In response, we have revised the manuscript to make these assumptions more explicit and have added numerical results for a quantum spin model to further support our conclusions. Detailed responses are provided below.
We thank Referee B for their positive assessment, noting that our work “addresses an interesting problem,” is “well written,” and “clearly outlines the parallel between the definitions proposed for open systems and the accepted ones for thermally isolated systems.” We also appreciate the referee’s request for a clearer discussion of the physical meaning of the properties we introduce. In response, we have expanded this discussion in both the main text and the present reply, added an explicit dissipative XXZ-chain example to demonstrate that the Loschmidt-echo dynamics we study are not specific to the SYK model, and clarified why we focus on cases where the steady state is independent of system parameters and dissipation—namely, to emphasize features that are not model-specific. The detailed arguments are provided in our reply.
With these revisions, we are resubmitting our improved manuscript for consideration in SciPost. We believe that the revised version better highlights the physical significance of our work and now meets the high standard for publication in SciPost.
Please find attached our point-by-point response to the referees’ comments, in which we address all of their concerns and indicate the changes made to improve our manuscript where appropriate. Should you require any further information, please do not hesitate to contact us.
Sincerely,
Yi-Neng Zhou and Chang Liu
List of changes
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We have added Loschmidt-echo simulation results for the dissipative XXZ model, together with a discussion of these points, to Appendix C. We have also revised the main text (by adding a paragraph at the end of Sec. 3, updating the introduction, and adding a second paragraph to the conclusions) to clarify that, although our explicit calculations are performed in the SYK and XXZ models, the underlying mechanism is general.
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We have added a discussion of the physical meaning of the Loschmidt echo in open systems to the main text, in Sec. 2 below Eq. (7).
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We include a brief comment in the final paragraph of Sec. 4 explaining that, since the LE–OTOC relation in open systems admits several reasonable generalizations, the specific relation we derive is not unique.
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We have added a sentence in Sec. 4.1 below Eq. (19) explaining the noise-averaged approximation, and we have inserted an additional intermediate step in Eq. (20) to make the derivation more transparent.
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We have incorporated a discussion of the operational meaning of the second Rényi entropy in open systems by adding a paragraph at the end of Sec. 5 of the main text.
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We have clarified how the time reversal required in our OTOC measurement protocol can be implemented, and we have added this explanation in the final paragraph of Sec. 6 of the revised manuscript.