Reply on "Comment on 'Role of initial entanglement and non-Gaussianity in the decoherence of photon-number entangled states evolving in a noisy channel' "

In a recent work (Allegra et al, Phys. Rev. Lett. 105, 100503, 2010) we addressed the evolution of photon-number entangled states in noisy Gaussian channels. Upon exploiting several non equivalent separability criteria we found evidence that entanglement of Gaussian PNES survives longer, and thus we drew a conjecture about the generality of this result. In their Comment to our work, Lee et al. use an additional entanglement criterion (NDPT) which allows them to show some counterexamples to our conjecture, i.e., nonGaussian states whose entanglement survives longer. In this reply, we argue that although there are no flaws or central errors in our original Letter, the conjecture is not maintanable in a strict sense if one includes the NDPT criterion. Nevertheless, for the examples of non Gaussian states proposed in the Comment, which violate the conjecture, the residual entanglement is extremely low. Therefore it remains an open question whether these, as well as other kinds of states, could represent a useful resource in quantum communication protocols.