Robustness of quantum key distribution with discrete and continuous variables to channel noise

TL;DR

This paper compares the robustness of discrete-variable and continuous-variable quantum key distribution protocols against channel noise, revealing conditions under which each protocol type performs better, especially considering practical resource limitations.

Contribution

It introduces a unified noise model for both protocol types and provides a comparative analysis of their noise tolerances under realistic conditions.

Findings

Continuous-variable protocols are robust at high transmittance.

Discrete-variable protocols outperform under strong loss conditions.

Practical photon sources can enable discrete-variable superiority.

Abstract

We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for continuous-variable quantum key distribution, to the discrete-variable case. Then we perform a comparison of the bounds on the tolerable channel noise between these two kinds of protocols using the same noise parametrization, in the case of implementation which is perfect otherwise. Obtained results show that continuous-variable protocols can exhibit similar robustness to the channel noise when the transmittance of the channel is relatively high. However, for strong loss discrete-variable protocols are superior and can overcome even the infinite-squeezing continuous-variable protocol while using limited nonclassical resources. The requirement on the probability of a single-photon production which would have to be fulfilled by a practical source of photons in order to demonstrate such superiority is feasible thanks to the recent rapid development in this field.