Finite‐Size Analysis of Thermal States Quantum Cryptography with the Optimal Noise

Abstract

A modified thermal states quantum cryptography is proposed by adding the noise at Bob's side and the impact of finite-size effects focused on by performing the channel estimation. An optimal noise which can maximize the key rate is demonstrated to exist and, by using numeric simulations, is shown to vary with the transmission distance. Adding the optimal noise can enhance the effectiveness of the thermal states quantum cryptography protocol under noisy and lossy channel in terms of secret key rate, the maximum transmission distance and the tolerable channel noise. Although finite-size effects deteriorate the performance of thermal quantum cryptography, this approach can compensate the impact of this degradation, and even make the performance of the modified protocol in the finite-size regime better than that of the original protocol in the ideal asymptotic regime.