Analysis of Subcarrier Multiplexed Quantum Key Distribution Systems: Signal, Intermodulation, and Quantum Bit Error Rate

This paper provides an in-depth theoretical analysis of subcarrier multiplexed quantum key distribution (SCM-QKD) systems, taking into account as many factors of impairment as possible and especially considering the influence of nonlinear signal mixing on the end-to-end quantum bit error rate (QBER) and the useful key rate. A detailed analysis of SCM-QKD is performed considering the different factors affecting the sideband visibility (drifts in the modulator bias points, modulation index mismatch between Alice and Bob subcarriers) and the impact of nonlinear signal mixing leaking into otherwise void subcarrier sidebands. In a similar way to classical photonic radio-over-fiber telecommunication and cable TV systems, the impact of this nonlinear signal mixing can be accounted in terms of a quantum carrier to noise ratio that depends on the specific frequency plan that is implemented. QBER and useful key rate results for three different frequency plans featuring $N$ $=$ 15 (low-count channel system), $N$ $=$ 30 (intermediate-count channel system), and $N$ $=$ 50 (high-count channel system) channels are provided, showing that photon nonlinear mixing can be of importance in middle- and high-count SCM-QKD systems ($N$ ≫ 30), with moderate RF modulation indexes ($m$ ≫ 5%). In practical terms, nonlinear signal mixing can be neglected if low modulation indexes ($m$ ≪ 2%) are employed to encode the photons in the subcarrier sidebands.