  Multi-carrier continuous-variable quantum key distribution (CV-QKD) is
considered to be a promising way to boost the secret key rate (SKR) over the
existing single-carrier CV-QKD scheme. However, the extra excess noise induced
in the imperfect multi-carrier quantum state preparation process of N
subcarriers will limit the performance of the system. Here, a systematic
modulation noise model is proposed for the multi-carrier CV-QKD based on the
orthogonal frequency division multiplexing (OFDM). Subsequently, the
performance of multi-carrier CV-QKD with arbitrary modulation protocol (e.g.
QPSK, 256QAM and Gaussian modulation protocol) can be quantitatively evaluated
by combining the security analysis method of the single-carrier CV-QKD. Under
practical system parameters, the simulation results show that the SKR of the
multi-carrier CV-QKD can still be significantly improved by increasing the
carrier number N even with imperfect practical modulations. Specifically, the
total SKR of multi-carrier CV-QKD can be optimized by carefully choosing N. The
proposed model provides a feasible theoretical framework for the future
multi-carrier CV-QKD experimental implementation.
