Qubit Clock in Quantum Cosmology

Round 1

Reviewer 1 Report

In this article the author considers a quantum cosmological model with a qubit clock, in order to study the emergence of a time parameter which defines the evolution of the wave function of the universe. The paper is based on Page-Wooters approach, and is a variation of a previous paper by the author [4], in which, instead of a qubit, an homogeneous quantum scalar field is coupled to gravity.

 I have some concerns regarding both the presentation and the relation with the previous work [4]:

1. The introduction is too short, and there is no mention to other approaches to introduce a time parameter in canonical gravity.
2. Where do Eqs.(14) and (15) come from? It is probably a definition of the parameter $T$. If this is the case, it should be properly stated. 
3.  I do not understand the definition given in Eq.(28). On the one hand, there seems to be a typo in the first equality. On the other hand, using the relation between $\psi$ and $\Psi_1$ and $\Psi_2$  I do not see how to obtain Eq.(29).
4. In the previous paper[4],  instead of a qubit, an homogeneous quantum scalar field is coupled to gravity. The Hamiltonian for a massive field is that of a harmonic oscillator, and the authors present explicit results for the conditioned wave functions for the case of two quantum harmonic oscillator eigenstates. Which is the relation between those results and the corresponding ones for the qubit? Which are the motivations to consider a qubit instead of a harmonic oscillator?

For these reasons, I cannot recommend pubblication of the article in its present form.

 

Author Response

We appreciate the anonymous referees for their critical comments which
are very helpful to improve our paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper discusses the proposal of having the quantum clock due to the entanglement of a qubit and the universe. Qubit acts as a clock and replaces the standard approach in quantum cosmology in which one of the variables in the hyperbolic Wheeler-deWitt equation becomes a time variable – usually it is the scale factor. The approach relies on the Fisher information matrix and has some drawbacks when it vanishes.

 

I like the idea and consider the paper publishable. However I have some comments to the Author to deal with:

 

1. In (12) the variable “z” is introduced, but it should be somehow related to “ρ” I guess. This should be clarified.

2. Standard quantum cosmologists use an abbreviation WdW rather than WD on Wheeler-deWitt.

3. The “time” parameter T is the function of the energy density (so, in fact also the scale factor) in (20). This is similar as in standard approach known from Ref. [1] but also in many papers by Kiefer for example. The Author should make some comparative discussion why his qubit clock is better clock than just one of the minisuperspace variables?

4. Also, he should cite more references related to the standard approach to the definition of internal time variable by the scale factor in WDW equation.

5. In (28) the wave function is dependent on the two variables: “ρ” and “T”, but by Author's assumption “T” is the function of “ρ”. So, why they are treated as independent?

6. In the abstract and twice in the text the Author uses the expression “...demonstrated THAT how etc.” I think “that” is a surplus here and should be removed.

 

Author Response

We appreciate the anonymous referees for their critical comments which
are very helpful to improve our paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have revised the manuscript according to the suggestiions in my previous report. I think is now suitable for publication.

Reviewer 2 Report

The paper has been improved according to my suggestions. I recommend publication.