Bounds on Probability of Detection Error in Quantum-Enhanced Noise Radar
Round 1
Reviewer 1 Report
This paper theoretically develops a model to describe the statistical behavior of the quantum enhanced noise radar model, in addition to discussing approaches such as the joint measurement model, and classical noise radar.
While there do exist related publications on this topic, this submission does an excellent job explaining the context of the research, as well as developing the theory. I recommend acceptance for publication. I do have some minor errors to report and some questions for the authors however:
- Is there any further development behind Equation (1)? There does not seem to be any citation associated with it. I assume |psi> is a two mode squeezed state emerging from an SPDC source. Is this equation an assertion from the author? Or an expression from another publication?
- Is there any kind of insight or explanation about the measurement operator M introduced on line 93? In other words, is there any information you can provide about how to implement this measurement in the laboratory? While not required at all for the scope of this paper, it would be interesting to know.
- The quantity rho in the covariance matrices is not defined. I believe it to be the correlation coefficient. Further, it is asserted in line 151 that rho^2 is typically very small. Can you explain why this is the case? Is this because of the low SNR nature of the detection?
- For Figure 2, in order to better exaggerate the difference between the two cases, it may be helpful to use a log scale. Also, in the description (and perhaps elsewhere) the word "exaggerate" is spelled incorrectly (There is only 1 g, when there should be 2.).
- Line 195 says "...is present them takes the form" the word "them" should be "then."
- Remnants of the article template remain in the acknowledgements section (line 326-328). Recommend deletion.
- In the appendix, Equation (A3), K0 is not defined. Namely, putting words like, "Where K0 is....."
Very good article!
Author Response
Review #1
The reviewer comments are in normal type. My responses are in bold type.
This paper theoretically develops a model to describe the statistical behavior of the quantum enhanced noise radar model, in addition to discussing approaches such as the joint measurement model, and classical noise radar.
While there do exist related publications on this topic, this submission does an excellent job explaining the context of the research, as well as developing the theory. I recommend acceptance for publication. I do have some minor errors to report and some questions for the authors however:
- Is there any further development behind Equation (1)? There does not seem to be any citation associated with it. I assume |psi> is a two mode squeezed state emerging from an SPDC source. Is this equation an assertion from the author? Or an expression from another publication?
Equation 1 is not an assertion by the author. It appears in various textbooks and review papers. A citation to reference 17 (now 18) in the original manuscript was intended to guide the reader to a useful textbook that covers this equation. However, the citation must have been located too far beyond the equation itself. Thus, I have moved it up in the sentence to just before Eq. 1. Also, I have added a second reference (now 17) that treats this equation in more detail and connects it to the more common photon-number representation of the two-mode squeezed vacuum. Finally, in the sentence that introduces Eq. 1, I have replaced the words “combined signal and idler system” with “two-mode squeezed vacuum”.
- Is there any kind of insight or explanation about the measurement operator M introduced on line 93? In other words, is there any information you can provide about how to implement this measurement in the laboratory? While not required at all for the scope of this paper, it would be interesting to know.
This is an interesting question. In response, I have added the following text at line 101 in the new version: “These states are not intended to represent physically realistic models of experimentally implementable devices. Rather, the goal is to define the detector states purely in terms of the optimum performance allowed by quantum physics. In effect, this is a limiting case in which no classical noise is added by the measurements and quantum noise is as weak as possible.”
- The quantity rho in the covariance matrices is not defined. I believe it to be the correlation coefficient. Further, it is asserted in line 151 that rho^2 is typically very small. Can you explain why this is the case? Is this because of the low SNR nature of the detection?
Unfortunately, rho was used to represent two separate concepts: (1) the density operator and (2) the amplitude reflection coefficient of the beam splitter model of loss and noise. To clarify the notation, I have adopted the notation of Ref. 14 where kappa is the power reflection coefficient or reflectance of the beam splitter. Kappa is the square of the coefficient formerly named rho. I have also removed the analogous transmission coefficient tau. What was tau^2 is now simply 1 – kappa. This change removes the overuse of rho, and aligns the notation better with the existing quantum illumination literature. All equations and figures have been revised to reflect this change of notation.
The value of the reflection coefficient (rho or kappa) is typically small because it represents all loss mechanisms and because losses are large in remote sensing. The following text has been added, beginning at line 124, to explain this in more detail: ”Losses in remote sensing are typically substantial. First and foremost, this is true because only a small fraction of the transmitted energy actually falls on the target and is reflected into the receiver. Some other sources of loss include absorption by the target or the atmosphere, detector inefficiency, multi-path fading, and Doppler shifts. Consequently, the reflectance kappa << 1.”
- For Figure 2, in order to better exaggerate the difference between the two cases, it may be helpful to use a log scale. Also, in the description (and perhaps elsewhere) the word "exaggerate" is spelled incorrectly (There is only 1 g, when there should be 2.).
The spelling error has been corrected. Both linear and log scales were considered for Fig. 2. The tails of the distributions are exponential, so on a log plot, the distributions look like triangles. Although a log plot does emphasize the differences between the distributions for target present and target absent, the linear plot was ultimately preferred because (1) it more immediately depicts the actual shape of the distributions, and (2) it emphasizes the similarity of the two case, which is exactly the reason why a quantum advantage would be sought in the first place.
- Line 195 says "...is present them takes the form" the word "them" should be "then."
This typo has been corrected.
- Remnants of the article template remain in the acknowledgements section (line 326-328). Recommend deletion.
The template acknowledgement has been replaced with a proper acknowledgement: “The author gratefully acknowledges discussions with Ned J. Corron and Shawn D. Pethel that were helpful in clarifying aspects of the model presented in this article.”
- In the appendix, Equation (A3), K0 is not defined. Namely, putting words like, "Where K0 is....."
The following text has been inserted directly after Eq. (A3): “where $K_0(x)$ is the zeroth-order, modified Bessel function of the second kind.”
Very good article!
Reviewer 2 Report
This is an excellent paper of timely interest in the new emerging area of quantum radar. The paper addresses the detection problem in quantum radar and develops the necessary analytical formulations from first principles in an elegant manner. Appropriate comparisons are made between different types of quantum radar approaches and also with their traditional counterparts, namely, noise radar. The theoretical results are very well illustrated using understandable graphical plots.
My only non-technical suggestion for the author is to delete the Acknowledgments section (lines 326-328) as this is not applicable or needed.
Author Response
Review #2
The reviewer's comments are in normal type. My responses are in bold type.
This is an excellent paper of timely interest in the new emerging area of quantum radar. The paper addresses the detection problem in quantum radar and develops the necessary analytical formulations from first principles in an elegant manner. Appropriate comparisons are made between different types of quantum radar approaches and also with their traditional counterparts, namely, noise radar. The theoretical results are very well illustrated using understandable graphical plots.
My only non-technical suggestion for the author is to delete the Acknowledgments section (lines 326-328) as this is not applicable or needed.
The template acknowledgement has been replaced with a proper acknowledgement: “The author gratefully acknowledges discussions with Ned J. Corron and Shawn D. Pethel that were helpful in clarifying aspects of the model presented in this article.”
Reviewer 3 Report
This work gave a model for analyzing detection error in quantum-enhanced noise radar. I think the argumentation of the author is valuable (though its correctness is ultimately his responsibility). It may be suitable for publication in Quantum Rep.Author Response
Review #3
The reviewer's comments are in normal type. My response is in bold type.
This work gave a model for analyzing detection error in quantum-enhanced noise radar. I think the argumentation of the author is valuable (though its correctness is ultimately his responsibility). It may be suitable for publication in Quantum Rep.
No specific issues are raised here. So no response is necessary.
