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QMetrology from QCosmology: Study with Entangled Two Qubit Open Quantum System in De Sitter Space

by Sayantan Choudhury, Satyaki Chowdhury, Nitin Gupta, Abinash Swain

This is not the latest submitted version.

This Submission thread is now published as SciPost Phys. Core 4, 006 (2021)

Submission summary

As Contributors: Sayantan Choudhury
Arxiv Link: (pdf)
Date submitted: 2020-10-21 11:42
Submitted by: Choudhury, Sayantan
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
  • Cosmology and Nongalactic Astrophysics
Approaches: Theoretical, Phenomenological


In this paper, our prime objective is to apply the techniques of {\it parameter estimation theory} and the concept of {\it Quantum Metrology} in the form of {\it Fisher Information} to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. {\it Quantum Metrology}, compared to {\it classical parameter estimation theory}, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper, we present a new avenue in terms of {\it Quantum Metrology}, which beats the classical parameter estimation. We also present an interesting result of \textit{revival of out-of-equilibrium feature at the late time scales, arising due to the long-range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2021-1-7 (Contributed Report)

  • Cite as: Anonymous, Report on arXiv:2005.13555v1, delivered 2021-01-07, doi: 10.21468/SciPost.Report.2383


In the paper the authors investigate the quantum metrological properties in dS space. They evaluate the attainable metrological gain for a 2 qubits system coupled to a thermal bath by using the Cramer-Rao bound of the Fisher information, both classical and quantum version. The authors discuss the performance of both Fisher information on few quantities such as the following terms I quoted directly from the paper: "Time scale, Euclidean Distance and Interaction Strength between the system and the ambient space-time."

The central idea of this paper is that one can still attain some useful information for metrological purpose even when coupled to bath is interesting. However, this idea has already been well studied in numbers of system such as spin squeezing using optical cavity. Except for the dS space that the authors discussed, I don't see any innovation in this manuscript. Also, the whole story of QFI is that people know there exists a way to gain information, but what actually matters is HOW to extract them. The authors did not discuss anything about it.

Speaking of the dS space, I don't see any reasons to study in this particular spacetime. Also, the paper is trying to understand the problem using quantum mechanics in dS space, which was not commonly used and the validity should be justified.

Some of the discussed quantities are barely explained.

There are also certain amount of formatting and writing problems.
- I was very lost in page 2-5; for example in page 4 it took me a while to realize that the bottom left part is the unfinished footnote in page 3. I think the authors should not write so long footnotes: if the contents are important please move them to the main text; otherwise please remove them.
- Also, I recommend the authors to remove the review of Fisher information and leave the necessary references should be enough.
- The authors should add paragraphs about quantum metrology in the introduction part.
- And the introduction in its current form contains too many unnecessary terms and abbreviations which are irrelevant to the whole paper, making it unreadable. In fact, there are way too many introduced concepts all over the paper, which are barely used later in the paper.

Requested changes

See report.

  • validity: ok
  • significance: low
  • originality: low
  • clarity: low
  • formatting: acceptable
  • grammar: below threshold

Author:  Sayantan Choudhury  on 2021-01-19  [id 1162]

(in reply to Report 2 on 2021-01-07)

Response to the referee is attached as .pdf file and submitted.



Anonymous Report 1 on 2021-1-3 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2005.13555v1, delivered 2021-01-03, doi: 10.21468/SciPost.Report.2353


1. As far as I understood, the authors are studying a quantum system. Hence it is a little bit confusing to me when they talk about using classical Fisher information and compare it with quantum Fisher information. They should clarify this point.

2. The definition of quantum Fisher information matrix given in equation (39) of the paper. Then for a using the spectral decomposition of the density matrix of the system it the takes the form mentioned in equation (47) and various terms in (47) are mentioned in (48), (49) and (50). The part mentioned in (48) is termed as "Classical Fisher Information." In equation (38), another definition of classical Fisher Information is given. How do these two things correlate?

3. Furthermore, in the subsequent section, the authors claimed that they had computed both the classical and quantum Fisher Information. I believe they have used (48) to compute the classical Fisher Information. Then where the discussion of section A of page-6 of the paper enters into the picture? If not, I will suggest removing that from the paper.

4. If what I mentioned in the previous point is correct then, there is no reason to only compute the first term (the classical part) of the equation (47) and then compare with the full expression. More clarifications are needed in this regard.

5. Last but not least, the significance of the result is not clear at all. There are already various works on Quantum Fisher Information where it is used to study the dynamics of a quantum system ( some of them are already cited in the paper itself) and its usefulness is also discussed. So what new things we learn from this exercise about the underlying system? Impact of the result mentioned in the paper is not very clear to me. Authors should expand upon on it.


Authors used Quantum Fisher Information for a two-qubit system coupled with a thermal bath. The bath is modelled by a conformally coupled scalar field on a background of de Sitter spacetime. They observe a revival while studying the system dynamics. The calculation seems to be reasonable, but the significance of the result, especially in the context of the underlying result is not very clear. Do we learn anything novel about the underlying system apart from observing the revival? Why this particular model is chosen ?. To me the significance and impact of the result is not sufficient enough to merit a publication in Sci-Post physics, I recommend this for publication in Sci-Post Physics core instead after clarifying the doubts.

  • validity: ok
  • significance: low
  • originality: low
  • clarity: ok
  • formatting: reasonable
  • grammar: reasonable

Author:  Sayantan Choudhury  on 2021-01-19  [id 1163]

(in reply to Report 1 on 2021-01-03)

Response to the referee is attached as .pdf file and submitted.



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Anonymous on 2021-01-09  [id 1130]


A comment from a Condensed Matter Theorist: it is very difficult to recognize anything relevant to "Condensed Matter Physics - Theory" in this manuscript. Hence, it is strange to see this specialty appear among the choices.

Anonymous on 2021-01-10  [id 1136]

(in reply to Anonymous Comment on 2021-01-09 [id 1130])

Thank you for asking such question. These days the presented type of work is a subject of interest of quantum information theory and condensed matter physics people as well. For this reason we have cross-listed the present work in the condensed matter physics theory category. I hope this clarifies the comment.