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

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.

See report.

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.