Dear Editor,

again we would like to thank the referees for their time looking at our revised manuscript and comments. To address their comments in this round:

1. Referee 2, typo: The double "the" in the implementation section got lost in the last revision, we fixed it now. 

2. Referee 2, doubts about the novelty of our approach (point 1):
We certainly state clearly that the physical basis of the random numbers, namely the vacuum fluctuations of the optical field at the local oscillator frequency, has been used before, and we believe we had referenced a lot of relevant work on this, including the references pointed out by referee 2. For an application, it is important to have an effective practical and fast randomness extraction scheme, and this is what we demonstrate in this work. While LFSR have been around for ages, we believe their use for this purpose makes fast randomness extraction very simple, even though much higher rates have been reported with what we believe are more complex methods.

3. Referee 2, doubts about the randomness extraction (point 2 and 3):
As stated in our earlier reply, we do not have a proof yet for the LFSR method to be a "good" extractor, hence we also can not state under what assumptions it works. What we assume (and state clearly in the manuscript) is that subsequent samples are independent; we believe it should be extended to an assumption that we receive a certain amount of conditional entropy for each sample (to take care of the residual correlations of adjacent samples), and extract a fraction of it with the LFSR mechanism. Of course tests are not a proof, but they are a very practical method to indicate problems - especially problems that are related with the low linear complexity of LFSR sequences. As long as there is an outstanding proof for the LFSR extraction mechanism, we  believe test suites are not an unreasonable way of identifying problems.

4. Referee 3, typos in equation (5):
There was a missing minus sign in the center expression, which we added in the revised version. As for the dimension of the sigma_q, we note that this is the dimensionless width of the distribution in ADC steps, which is set to unity by default. As correctly pointed out by the referee, the entropy depends the ADC resolution. This is captured by how we define sigma (in steps of the ADC), so the right part of the equation is correct. We added a sentence ("Note that in (4) and (5), \sigma_q is measured in ADC steps; thus, with increasing converter resolution, the number of extractable random bits increases for a fixed noise amplitude.") after equation (5) to make this more obvious.

With this, we hope to have adequately addressed the concerns of the referees that can be addressed, and look forward for your reply.

With Best Regards on behalf of all authors,

Christian Kurtsiefer