Dear Editor,

we first like to thank the reviewers for their time and suggestions, and would like to take on your offer to transfer our manuscript to Physical Review Applied.

Please find below our responses(R) to each of the questions(Q) raised in the review.

Ref A Q1: Looking closely at reference [15], which is unfortunately only cited in the caption of figure 1, it seems to me that the idea of using thermal light for range finding was suggested (and demonstrated in a different setting) already.
Reply: The highlighted reference [15] describes a timing-delay measurement in optical fiber of about one kilometer. 
Although it also employs a time-of-flight measurement, typical range finding is performed in free-space which we demonstrate. The return loss in a non-lab based free space range finding measurement is significantly larger, and does require a significantly higher brightness that our source provides in comparison to the modulated light source (ground glass plate approach in [15]). As such, we feel that the experiment we present is at the very least a significant improvement in practicality, as we are able to cover realistic return losses.

Ref A Q2: The idea of using sub-threshold laser diodes for generating thermal light is not new by itself.
Reply: Subthreshold laser diode generation of thermal light is indeed known but to our knowledge has not been previously employed, due to the wider spectral output in subthreshold resulting in short coherence timescales.
This causes the temporal photon bunching effect to be unresolvable by single-photon avalanche detectors.
We address this problem by narrow-band spectral filtering using Fabry-Perot etalons with interference bandpass filters.

Ref A Q3: In the introduction, the authors write: ‘We demonstrate quantum sensing using a relatively simple thermal light source based on a sub-threshold diode laser.’. The meaning of quantum sensing in this context is not completely clear to me. What is quantum about this result?
Reply: The timing correlation in photon pairs in this work is due to the photon bunching effect of thermal light. While the thermal fluctuations can be described as classical fluctuations, the origin of the thermal light in our case is a level of spontaneous emission in the laser system, and as such in our view as "quantum" as the spontaneous parametric conversion in SPDC sources. The theory of photon bunching was developed in the 1960s by Roy Glauber to describe measurements of the 'coherence' of light from black body sources, and it was a major contributor to the field of quantum optics. Incidentally, the (pseudo-)thermal light generated by modulating a light beam with a ground glass disk, and perhaps the scattering of light from a suspension of scatterers in a liquid may be considered more as a "classical" as a classical modulation, with a - at least in the first case - clearly deterministic light field if the grinding pattern is known well enough.  The question is certainly interesting on a fundamental level, but we do stand by our claim that the correlations we observe in our thermal light source have a quantum origin. In this sense, we feel it is fair to compare that thermal light as a "quantum" resource of timing-correlated photons alterative to SPDC light, which justifies a discussion in the context of quantum sensing. The demonstration of range finding here is just an example. Clock synchronization would be another example for future demonstration. That said, we do feel that quantum sensing a such has probably a less obvious or widely accepted definition as one would like to in physics, and we hope to perhaps contribute to a necessary discussion with our work.

Ref A Q4: The authors chose to work at a current very close to the threshold of the diode. Could they comment on the reasons and trade-offs leading to the choice of the particular current?
Reply: The motivation to operate near the threshold of the diode is two-fold:
Firstly, operation needs to be below the lasing threshold of the diode, in order for the output light to exhibit photon bunching behavior which is necessary for the timing-correlation.
Secondly, our operating current is as high as possible, or close to the threshold, so as to maximize the output power and hence signal-to-noise ratio to increase the distance in ranging measurements. We are currently working on a more detailed experimental assessment of this near-threshold behavior of the photon statistics, but we feel that this work would exceed the scope of the more practical application in this manuscript.

Ref A Q5: Adding a more detailed comparison of the accuracy and signal to noise ratio of this method compared with common others could be useful. The comparison with SPDC sources for example is given mainly in terms of spectral density.
Reply: Range finding using SPDC light, sometimes referred to as "quantum radar", has been widely hypothesized and discussed. However, we are not aware of working demonstrations of this concept beyond table-top setups in the laboratory environment.
In this work, the thermal light source exhibits 10 orders of magnitude improvement in spectral density due to longer coherence timescale and bright output intensity have resulted in significantly higher signal-to-noise ratio. We demonstrate that this is sufficient to work outside the lab environment, by demonstration over a kilometer across a bay water outdoor environment. We believe this provides evidence for considering thermal light as a practical resource to SPDC light in some quantum sensing protocols.

Ref A Q6: The authors should comment on the applicability of this method for real-life scenarios. In the current experiment, a retroreflector is used as a target, probably in order to enhance the returning signal. What are the limits of the current method and source for real targets? How does it compare to current state-of-the-art schemes?
Reply: In this work, we compare thermal light sources to SPDC light sources in a quantum sensing protocol, rather than as an alternative to modulated light in conventional optical ranging. Therefore, the comparable scenario in current state-of-the-art would be a quantum radar which - to our knowledge - remains confined to laboratory environments on the meter-scale and require a more complex light source. A comparison with "conventional" off-the-shelf range finding systems that simply modulate a light source with a suitable deterministic pattern, will in many scenarios very likely still exhibit a higher signal-to-noise ratio, simply because the correlation of the signal with its reference can be arbitrarily high.  


Ref B Q1: Range finding has been demonstrated earlier using spontaneous parametric down-conversion (SPDC). The paper I mean, S. Frick et al., Optics Express 28, 37118 (2020), is surprisingly not cited by the authors; they do mention SPDC-based range finding but the papers they cite (Refs. 5,6) are on another subject.

Reply:  We thank the referee for pointing out this reference, and included it for examples of SPDC-based ranging. To our understanding, this experiment demonstrates SPDC-based ranging in free-space over 3-meters in a lab, with a resolution of 10 cm, and states explicitly: "In our protocol, entanglement is not used to improve the SNR compared to single-mode illumination schemes." We feel this statement supports our claim that the main aspect of SPDC sources for ranging is indeed the temporal correlations. We feel it would be unfair to include it into figure 1, as the source there was not particularly bright in terms of spectral density ("a maximal event rate of ≈1MHz", bandwidth not explicitely mentioned, but from related texts of the authors we infer 200nm), which would likely position SPDC sources unfairly.


Rev B Q2: The authors claim that thermal sources are more practical because they can be bright and narrowband; here they use a diode laser below threshold. Such sources, however, are known; for instance, the authors of A. Jechow et al. Nat. Photonics 7, p. 973 (2013) used thermal light from a similar below-threshold laser to pump second-harmonic generation.

Reply:  We thank the referee for highlighting this work. To our understanding, the light source used there is a superluminescent diode (SLD), but not really a subthreshold laser. Such light sources are indeed are very similar to sub-threshold lasers in that they both produce amplified spontaneous emission.
However, the SLD output spectrum is about 20 nm wide, corresponding to a coherence time below 100fs. While this permits a very high time resolution, the g2 correlation equally very narrow, so the authors elegantly carry out the coincidence  detection through a two-photon absorption process. Most photodetectors used for this trick have a very low probability/efficiency per detection event in comparison to a direct coincidence measurement of events seen by single photon detectors. Furthermore, the scheme requires an optical delay on the reference arm as well to ensure arrival of the bunched photons at the same time on the two-photon detector. To our understanding, it will therefore be challenging to apply this scheme to longer distances, as it requires to physically scan the reference arm across the whole range of interest.


Ref B Q3: Advantage of stationary light sources, eavesdropping discussion Reply: Contrary to quantum communication, the vulnerability of a ranging measurement is susceptible to different attacks, that likely go beyond the scope we cover in this manuscript. For all schemes, insertion of an optical delay line is possible and can lead to a misreading of a length. Also, access to a fraction of the light of the transmitter would not necessarily be overly useful, as such an attack would at most only result in access to the same information that could be obtained by a measurement of an eavesdropper alone. We do see, however, an advantage in stationary, non-deterministic light fields and utilizing their correlations due to resilience against falsification attacks on known modulation codes, or perhaps more practically to prevent interference from different sensors in a lidar scenario from several vehicles. Here, light from SPDC sources and thermal sources share the same robustness, and have an advantage compared to the deterministically modulated light sources in conventional lidar systems, but we do not see the advantage of an SPDC source compared to a thermal source with respect to eavesdropping attempts the referee suggests. In direct comparison, SPDC sources show stronger correlations in photodetection time (basically, a very high coincidence-to-accidental ratio), while thermal light sources can be made spectrally very bright with a comparatively smaller effort.

Ref B Q4: Quantum sensing
Reply: We partly understand the unhappiness with the notion quantum sensing, and believe this is possibly due to lack of a consensus on a definition what is really meant by that. As argued above, we feel that the "quantum" part in the light source we use is very comparable to SPDC sources, where range finding has been announced as quantum sensing application in the past by several groups {ref}. We thought about replacing quantum sensing in the title with something less controversial, but that is something that would apply to many papers in the field, and therefore are inclined to keep the title.  We do see an advantage in a non-deterministic light field and utilizing its correlations due to resilience against attacks on known codes both with SPDC and thermal light lidars, and feel both belong to a similar class that has been framed in a quantum sensing context precisely to highlight what correlations are used in both cases, and leave the discussion and comparison in the main text.


Ref B Q5: Cavity-generated CW squeezed vacuum.
Reply: We agree with the referee, and did include a to our knowledge specific reference to such a source both in the figure and the main text (new Reference 22: T.J. Steiner et al., Ultrabright entangled photon pair generation..., PRX Quantum 2, 010338 (2021).)

Changes on the manuscript:
1. We reformatted the manuscript to fit to Physical Review Applied (mostly introduced appropriate section headings).
2. We modified figure 1 to include the cavity-enhanced parametric down conversion reference 22, modified the figure caption accordingly, and added the reference to this recent work.
3. We added a qualifier "most" to the last sentence of the introduction, as our source is indeed only around 8 orders of magnitude brighter than the SPDC source in reference 22. 

With this, we hope to have addressed the comments from the referees, and hope for a favorable consideration for publication in Physical Review Applied.

With Best Regards on behalf of all authors,

Christian Kurtsiefer