Robust Phase Estimation of Gaussian States in the Presence of Outlier Quantum States

Round 1

Reviewer 1 Report

This manuscript deals with parameter estimation in the presence of the "outlier quantum states". It first presents the M-estimator theory and later applies it to the estimation of the phase of a coherent state, mixed with a thermal state (all single-mode electromagnetic field). 

Here are some remarks, from the point of view of a person that works on quantum theory and quantum metrology. The "theory" sections are unreadable to me. They are way too technical and often unclear. Why, for instance, above line 79, c=4.68*theta and gamma=0.2? This is not obvious and there are other examples of such unclear choices later in the text. Below Eq.4, Authors say that when |x|-->\infty, \psi_bi vanishes smoothly. But it seems not to be the case. As a general, section 2 and 3 seem unclear for me.

Later, Authors introduce their model. First, I am not familiar with the concept of an "outlier state". As I see from Eq.(17) this is just an admixture of some state (in this case thermal) to the ideal one, which contains the parameter. But what is the physical mechanism leading to such a system. Is this the traced-out environment? If so, what kind of environment it is? Or is it just a thermal excitation of a photonic state?

As Authors see, I had problems in understanding the model and the physics behind. Perhaps a more statistical-science-oriented referee could provide a more insightful report. From my perspective, this work does not deserve to be published in Applied Sciences. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors study the problem of imperfection at the stage of quantum state preparation, which generates unwarranted outlier quantum states at random. They present a statistical framework of robust statistics to handle outlier quantum states in a quantum system and implement the method of M-estimators to suppress untrusted measurement outcomes due to outlier quantum states. Among two studied specific M-estimators, bisquare and gamma, the authors have found that the application of gamma M-estimator leads to most accurate results.

The article is well-organized and the results are clearly presented.

As a minor suggestion, I would like to recommend careful English correction before publication. A few examples:

line 53: "In stead" should be "Instead"

lines 84-85: "and found that the same conclusion" should be "and reached the same conclusion"

line 124: "we have a short discussion on evaluation of robustness" should be "we discuss briefly the evaluation of robustness"

line 238: "We next plot" should be "Next, we plot"

line 241: "gamma M-estimators are the most robust estimator" should be either "gamma M-estimators are the most robust estimators" or "gamma M-estimators perfom most robustly"

lines 264-265: Section 5.5. Discussion "We now discuss our results." This first sentence is obvious and can be deleted. The section is titled "Discussion" so it is only natural that what follows in the text will be the authors to discuss their results.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf