Dear Editor,

We thank the reviewers for their comments.

Reply to Referee 1:

We thank Referee 1 for the insightful comments and for bringing to our attention the works of Zhang's group. They are very relevant and we are happy to cite and compare their results with the one presented in this manuscript.

Here follows our reply to the specific issues raised by the referee.


 - "In their manuscript, the authors presented that they used a simple point-to-point single mode optical connection based on bidirectional exchanging the SPDC photons, which seems that the quantum two-way time transfer is investigated for the first time in this paper. In fact, the two-way quantum clock synchronization protocol was proposed as early as 2017. A raw theoretical analysis was demonstrated on the conference of Quantum Information and Measurement 2017 (https://www.osapublishing.org/abstract.cfm?uri=QIM-2017-QF3A.4). A first experimental demonstration of the two-way quantum clock synchronization on a fiber coiling link of 20km with two clocks locked to a common frequency reference was presented on the conference of CLEO Pacific Rim 2018 (https://www.osapublishing.org/abstract.cfm?uri=CLEOPR-2018-Th4J.3). The most recent result based on the same setup can be found on arXiv (1812.10077), which achieves a time transfer time deviation of 922 fs at 5 s and 45 fs at 40960 s. I think these work should be cited and the authors may need limit their discussion to the condition of comparing two different clocks."

Indeed it appears that we developed this idea in parallel to related work by Zhang's group. 
We presented on the topic "Entanglement-Based Secure Quantum Clock Synchronization" at the QuantaLab Workshop [http://www.quantalab.org/quantalab-workshop-2017/] in September 2017 and were unaware of the related work. 
We subsequently presented it at an SPIE conference with associated proceedings [https://www.spiedigitallibrary.org/conference-proceedings-of-spie/10547/105470L/Secure-quantum-clock-synchronization/10.1117/12.2290561.short?SSO=1] and at Photonics West [http://spie.org/conferences-and-exhibitions/past-conferences-and-exhibitions/photonics-west-2018], both in January 2018. 
Our first experimental results appeared in the Institute of Physics Singapore Conference (IPS) [http://www.ipsmeeting.org/download/IPSMeeting2018.pdf] and the International Conference on Quantum Communication, Measurement and Computing (QCMC) [http://qcmc18.phys.lsu.edu/posters.pdf], both in March 2018. The results that are presented in this paper appeared in the arxiv [arXiv:1808.09019] on 20th December 2018, several days prior to the arxiv paper referenced above. To account for the results from Zhang's group, we have edited the introduction to highlight the initial proposal for a SPDC-based bidirectional time synchronization protocol by Hou et al. (2017), and included the experimental demonstration by Feiyan at al. (2018) and Hou et al. (2018) in the description of the state of the art.

We thank the Referee for the suggestion on how to frame the scope of our work, but we think that it is not necessary to limit the discussion to the comparison of different clocks. Our work shares some of the ideas presented by Zhang's group, but it was developed independently and relies on different and often more accessible technologies, achieving time resolutions consistent with the technologies used.

We modified section IV.A to include a comparison of the single time reference results with the homologous results in Hou et al. (2018).


- "Based on the equation (8) in the manuscript and the value given afterwards, it's hard to say what the sigma refers to, the FWHM width or the natural width. If it's FWHM width, which seems coincident with the expression in Eq. (8), then the value should be 683 ps instead of 290 ps. Please check it carefully and make a correction."

For the PseudoVoigt function, \sigma corresponds to half of the FWHM. We have clarified this relation in section III. We confirm that the value of \sigma, as expressed in Eq.(8) is 290 ps, corresponding to a PseudoVoigt FWHM of 580 ps.


- "Using the characterized precision of δt and pair rate of 200 s -1 , the timing response parameter of 1.65 ns -1 cannot be extracted based on Eq. (9). Could the author please explain why it doesn't coincide?"

We thank the Referee for pointing out this calculation error. The correct value is 0.81 ns-1. We amended the manuscript accordingly.


Reply to Referee 2:

We appreciate Referee 2's remarks on the thoroughness of our work. We also agree with the Referee that "providing first results on more sophisticated (asymmetrical) attacks would make the article more interesting." However, our intent for this paper was to demonstrate the soundness of the main synchronization protocol in sufficient technical detail, particularly the distance independence aspect, which is relevant to many applications, but can also be understood as a particular class of attack by a malicious party. An asymmetric attack demonstration is definitely of interest, but we intend to address the security aspects of clock synchronization (including different classes of attacks) in separate work, as this deserves its own in depth exploration. Recently, our group published the theoretical basis for detecting an asymmetric attack on arXiv [arXiv:1808.09019]. We intend to confirm the results experimentally in a separate manuscript.