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Quantifying Non-Markovianity in Open Quantum Dynamics
by Chu Guo
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Submission summary
| Authors (as registered SciPost users): | Chu Guo |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2205.05970v1 (pdf) |
| Date submitted: | May 17, 2022, 8:27 a.m. |
| Submitted by: | Chu Guo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.
Current status:
Has been resubmitted
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-6-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2205.05970v1, delivered 2022-06-22, doi: 10.21468/SciPost.Report.5270
Strengths
The paper is clear, complete and exhaustive.
The paper is timely as a lot of work is being dedicated recently to an MPO characterization of non-Markovian time evolution, see e.g. Pollock, PRA 97 012127 (2018); Sonner, Annals of Physics 431 168552 (2021); Guo arXiv:2203:01492 and related works.
The paper is timely as a lot of work is being dedicated recently to an MPO characterization of non-Markovian time evolution, see e.g. Pollock, PRA 97 012127 (2018); Sonner, Annals of Physics 431 168552 (2021); Guo arXiv:2203:01492 and related works.
Weaknesses
The paper does not offer a direct comparison of the two proposed non-Markovianity measures with other quantities proposed in the literature (such as the one in Breuer, PRL 103 210401 (2008) ).
It is therefore not clear whether the presented criteria are more stringent or more relaxed in measuring non-Markovianity.
It also seems that the complexity is still exponentiall in the spatial size of the system, as each evolution operator of the process tensor is still an operator acting on the Hilbert space of the system; this fact is still crucial when doing numerical simulations and should be stated more clearly.
It is therefore not clear whether the presented criteria are more stringent or more relaxed in measuring non-Markovianity.
It also seems that the complexity is still exponentiall in the spatial size of the system, as each evolution operator of the process tensor is still an operator acting on the Hilbert space of the system; this fact is still crucial when doing numerical simulations and should be stated more clearly.
Report
The paper presents an MPO (and MPDO) representation of the process tensor of the non-Markovian dynamics of a generic open quantum system. This representation is used to define two quantities which quantify the temporal entanglement of the evolution and may be used to characterize the degree of non-markovianity of the system.
The idea is that an MPO naturally describes the degree of entanglement of an operator, akin to what happens for MPS and MPOs in the usual DMRG description of the spatial correlations of a system; in such a sense a state with zero temporal entanglement corresponds to a completely factorizable evolution which corresponds to Markovian dynamics.
The advantage of the proposed non-Markovianity measures is that they scale polinomially in the evolution time instead of exponentially as in other measures.
I recommend publication of the manuscript in SciPost Physics.
The idea is that an MPO naturally describes the degree of entanglement of an operator, akin to what happens for MPS and MPOs in the usual DMRG description of the spatial correlations of a system; in such a sense a state with zero temporal entanglement corresponds to a completely factorizable evolution which corresponds to Markovian dynamics.
The advantage of the proposed non-Markovianity measures is that they scale polinomially in the evolution time instead of exponentially as in other measures.
I recommend publication of the manuscript in SciPost Physics.
Report #1 by Anonymous (Referee 1) on 2022-6-14 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2205.05970v1, delivered 2022-06-14, doi: 10.21468/SciPost.Report.5234
Strengths
- This work provided a method which can be efficiently computed based on the MPO represenation of the process tensor
- The computation complexity does not diverge exponentially with the evolution time steps
Report
Quantitatively characterizing the non-Markovianity of a dissipative quantum dynamics is one of the most important topics in the field of open quantum systems. In one of previous work (Ref.[16] in the reference list) , the authors proposed a necessary and sufficient quantum Markov condition based on a process tensor. Such a procedure, even though is sufficiently general, is very difficult, if not impossible, to be implemented in actual calculations, even for simple cases.
The present manuscript by Chu Guo addressed this issue, where he proposed two non-Markovianity measures based on the "entanglement" of the correpsonding MPO representation of the process tensor, which can be used to characterize the "memory effect" of the quantum dynamics. In this measurement, the Markov limit is approached if the process tensor can be written as a separable tensor product state. The application of this method on a concrete example of a two-spin system has also been discuss.
In my opinion, the advantage of the method are two-fold: it can be efficiently computed based on the MPO represenation of the process tensor and the computation complexity does not diverge exponentially with the evolution time steps. For this reason, i think this work is an important advance in the field of open quantum system and recommend the publication of this paper.
The present manuscript by Chu Guo addressed this issue, where he proposed two non-Markovianity measures based on the "entanglement" of the correpsonding MPO representation of the process tensor, which can be used to characterize the "memory effect" of the quantum dynamics. In this measurement, the Markov limit is approached if the process tensor can be written as a separable tensor product state. The application of this method on a concrete example of a two-spin system has also been discuss.
In my opinion, the advantage of the method are two-fold: it can be efficiently computed based on the MPO represenation of the process tensor and the computation complexity does not diverge exponentially with the evolution time steps. For this reason, i think this work is an important advance in the field of open quantum system and recommend the publication of this paper.