Derivation of rate equations: Corrections and further comments

Konstantin Kravtsov, S. N. Molotkov

In reply to the Comment by D. A. Kronberg [Phys. Rev. A 104, 026401 (2021)], we would like to reassure readers that none of the critiques actually apply to our final result of the security analysis, namely, Eq. (30). The major part of the Comment, as well as the conclusions, are derived from the consideration of the multiphoton component, which does not appear in our final result. At the same time, we admit that our original interpretation of multiphoton terms in Eq. (26) as well as the potential extension of Eq. (30) with such terms were not correct. The single-photon component plays an essential role in quantum key distribution and was the only one to appear in the final key rate equation, which is valid against the most general collective attack. The Comment concludes that Eq. (30) ``is incorrect ... and the security proof ... is not complete,'' which, as we show, is not the case.

R. L. Ingraham

Antoine Tilloy

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter $\ensuremath{\theta}(0)$ is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This Comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way, and finally shows where the main mistake of the authors of the original article was made.

Paul Kinsler, P. D. Drummond

We comment on statements made about quantum representation theory in the paper by T. W. Marshall and E. Santos [Phys. Rev. A 41, 1582 (1990)]. Results are presented which show that correct results can be obtained from Langevin equations derived from the positive-P representation, even when those obtained by truncation of the Wigner time-evolution equation give incorrect results.

John A. Happel