Quantum Non-Markovian Environment-to-System Backflows of Information: Nonoperational vs. Operational Approaches
Round 1
Reviewer 1 Report
The article “Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches” contains a review of results obtained on Markovian vs. non-Markovian behavior of system-environment ensembles. It takes into account two qualitatively different approaches and describes the results that can be obtained for different classes of models describing the environment and the interaction. The general conclusion is that outside of the Born-Markov approximation, providing a general classification of models which can only be Markovian or non-Markovian is extremely hard, as in most situations the models can display both types of dynamics.
The article provides a good introduction followed by the comparison mentioned above and is interesting to read. Although (as the author admits) no new results are presented, I believe that the comparison of different situations which is provided and the commentary are of undeniable scientific value.
The only scientific comment that I have is that casual bystander environments can in fact be entangled with the system, as long as the system is larger than a qubit [see K. Roszak, Criteria for system-environment entanglement generation for systems of any size in pure-dephasing evolutions,
Phys. Rev. A 98, 052344 (2018)], contrarily to what is stated in the first sentence of section 3.3. Undeniably all of the examples discussed in section 3.2 involve only separable states, but the property is not fully general.
The paper contains a lot of typos, [e. g.
line 120: determined
158: does not evolves
181: does not has
above eq. 27: does not implies
These are just some examples (I started writing them down only after page 3).]
but in general it is well written and understandable and they can be corrected on an editorial level.
In conclusion, I think that the article can be published as is.
Author Response
The manuscript has been reviewed by three Referees. Two of them considered that the manuscript is appropriate for publication. Specifically, the first Referee considers that thecontent of the manuscript is of undeniable scientific value and that the article can be published as is. In the view of the second Referee, it is expected that the manuscript to be well cited and influential, and also recommended publication by Entropy. On the other hand, the third Referee considers that the manuscript is well written, easy to understand and technically correct. In addition the Referee considered that a specific example must be added in order to obtain a more robust comparison between the different approaches.
The first Referee sent a very interesting scientific comment and a related paper. In the new manuscript version I introduced a few related comments, as well as the new Reference [37].
Let me remark that the comment of the first Referee is completely right. In fact, for very specific environment initial conditions, a unitary dynamics may not induce any system-environment entanglement (see new comment in head of Sec. 3.3). On the other hand, the conditions that define a casual bystander environment must be valid for arbitrary environment initial conditions. This important issue was clarified in the new sentence in the head of Sec. 3.2.
Following the Referees comments, typos and English redaction were checked in detail. In agreement with the Third Referee demand, I added new Section IV. The main changes are written in blue. In conclusion, I am confident that the manuscript deserves publication in its present form.
Reviewer 2 Report
Quantum non-Markovian behaviour and related memory effects belong to a class of central problems for quantum information processing, quantum statistical physics and theory of open quantum systems. The paper under consideration contains a comparative study of two memory-effect quantifiers: the first, non-operational, based upon trace distance as natural geometric measure with a clear physical interpretation, the second, operational, based on past-future correlations. The common context inducing non-Markovianity is a presence of information flow from environment to the system. Such an information flow affects memeory effects and their quantifiers and it is directly related to the type of environment and mechanism of system - environment coupling. The Author provides a well selected comparison of various environmental models and their impact on two above mentioned quantifiers of the memory effects. The paper is well written and fairly complete. The models considered in the work belong to a wide and important class. I expect the paper to be well cited and influential also because of its pedagogical aspect. I recommend its publication by Entropy.
Author Response
The manuscript has been reviewed by three Referees. Two of them considered that the manuscript is appropriate for publication. Specifically, the first Referee considers that the content of the manuscript is of undeniable scientific value and that the article can be published as is. In the view of the second Referee, it is expected that the manuscript to be well cited and influential, and also recommended publication by Entropy. On the other hand, the third Referee considers that the manuscript is well written, easy to understand and technically correct. In addition the Referee considered that a specific example must be added in order to obtain a more robust comparison between the different approaches.
Following the Referees comments, typos and English redaction were checked in detail. In agreement with the Third Referee demand, I added new Section IV. The main changes are written in blue. In conclusion, I am confident that the manuscript deserves publication in its present form.
Reviewer 3 Report
As it is acknowledged by the author himself, this work essentially presents a comparative analysis between operational and non-operational approaches to the problem of system-environment problem, which requires non-Markovian conditions to properly describe such backflow of coherence from the environment to the system. To this end, the causal bystander environmental model as well as other models are analyzed for the purpose of such a comparison.
The work might have some interest to the Entropy readership, in particular the quantum foundations and quantum information communities. It is well written, easy to understand, and, as far as I have checked, also technically correct (actually, it is based on former works by the same author on the issue, which have already been published recently). Now, the main inconvenience that I find here is that the work does not go beyond a superfluous comparative analysis disregarding any more robust quantitative comparison based on the analysis of a specific model from both approaches. As an interested reader myself, this is what I would expect after the operational and non-operational approaches have been introduced, and more specifically after having warned at the beginning that a comparison and analysis is going to be given. Without such a direct quantitative analysis, this manuscript does not go beyond a descriptive report-type work (compare, for instance, the present work with the work reported by the same author in Ref. 30).
Author Response
The manuscript has been reviewed by three Referees. Two of them considered that the manuscript is appropriate for publication. Specifically, the first Referee considers that the content of the manuscript is of undeniable scientific value and that the article can be published as is. In the view of the second Referee, it is expected that the manuscript to be well cited and influential, and also recommended publication by Entropy. On the other hand, the third Referee considers that the manuscript is well written, easy to understand and technically correct. In addition the Referee considered that a specific example must be added in order to obtain a more robust comparison between the different approaches.
In disagreement with the Referee, I don’t consider that the comparison between both approaches is superfluous. While the underlying results were obtained previously, an explicit comparison for different class of models is novel. On the other hand, in agreement with the Referee, I added new Section IV, which includes two new figures. I study a system coupled to an incoherent-coherent environment defined by four levels. The system dynamics turn out to be a depolarizing map. It is shown how both approaches differ in both in the Markovian vs non-Markovian classification of the dynamics as well as in the presence or absence of information backflows.
Following the Referees comments, typos and English redaction were checked in detail. The main changes are written in blue. In conclusion, I am confident that the manuscript deserves publication in its present form.
Round 2
Reviewer 3 Report
I considered that the previous comparative analysis was superfluous, because it did not go beyond a bare comparison. After the revision, I find the work worth publishing, because now the autho goes beyond a general comparison, providing the potentially interested reader with the added value of a specific application. Therefore, I recommend the work for publication in the present form.
