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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 |
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| Preprint Link: | https://arxiv.org/abs/2205.05970v2 (pdf) |
| Date accepted: | 2022-07-26 |
| Date submitted: | 2022-07-25 04:53 |
| Submitted by: | Guo, Chu |
| 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.
Author comments upon resubmission
Reply to Referee 1: I am very grateful for your positive assessment of this work and recommendation to publish on Scipost Physics Reply to Referee 2: I am very grateful for your positive assessment of this work and recommendation to publish on Scipost Physics with some minor comments, which are addressed as follows: 1) "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" Answer: I thank the referee for this comment. I thus add the last paragraph in the subsection "Reexamining the quantum dephasing dynamics" in the revised manuscript. Basicaly, the Breuer criterion for non-Markovianity will given 0 for both cases considered, namely both models would be considered Markovian due to Breuer criterion. In comparison, with our criterion, one of the two models is Markovian and the other is not. 2) "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" Answer: I thank the referee for this comment. Indeed the complexity (of computing the non-Markovianity measures and of the reconstruction algorithm for the hidden MQE) will be exponential with respect to the spatial size of the system in case the system itself is a many-body quantum instead of a single qubit (In the previous manuscript we mainly consider the complexity scaling against the number of time steps). As suggested, I added the second paragraph in the second paragraph in the section "EXAMPLES" to stress the exponential grow of complexity against the spatial dimension of the system in the revised manuscript.
List of changes
1. The second paragraph in the section "EXAMPLES" is newly added (at the end of the right column on Page 6 and the beginning of the left column on Page 7 )
2. The last paragraph in the subsection "Reexamining the quantum dephasing dynamics" is newly added (at the end of the right column on Page 8)
3. Several words as well as several citations are adjusted (updated) throughout the manuscript.
Published as SciPost Phys. 13, 028 (2022)