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

TL;DR

This paper defends the original findings that Gaussian photon-number entangled states maintain entanglement longer in noisy channels, while acknowledging that non-Gaussian states can sometimes outperform them, though with limited residual entanglement.

Contribution

It clarifies the validity of the original conjecture under different entanglement criteria and discusses the practical relevance of non-Gaussian states with longer entanglement survival.

Findings

Gaussian states have longer entanglement survival in noisy channels.

Non-Gaussian states can sometimes have longer entanglement, but residual entanglement is very low.

The conjecture's strict validity depends on the entanglement criterion used.

Abstract

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.