Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator

Recently, we proposed a simultaneous quantum and classical communication (SQCC) protocol, where random numbers for quantum key distribution (QKD) and bits for classical communication are encoded on the \emph{same} weak coherent pulse, and decoded by the \emph{same} coherent receiver. Such a scheme could be appealing in practice since a single coherent communication system can be used for multiple purposes. However, previous studies show that the SQCC protocol can only tolerate very small phase noise. This makes it incompatible with the coherent communication scheme using a true local oscillator (LO), which presents a relatively high phase noise due to the fact that the signal and the LO are generated from two independent lasers. In this paper, we improve the phase noise tolerance of the SQCC scheme using a true LO by adopting a refined noise model where phase noises originated from different sources are treated differently: on one hand, phase noise associated with the coherent receiver may be regarded as \emph{trusted} noise, since the detector can be calibrated locally and the photon statistics of the detected signals can be determined from the measurement results; on the other hand, phase noise due to the instability of fiber interferometers may be regarded as \emph{untrusted} noise, since its randomness (from the adversary's point to view) is hard to justify. Simulation results show the tolerable phase noise in this refined noise model is significantly higher than that in the previous study where all the phase noises are assumed to be untrusted. We conduct an experiment to show the required phase stability can be achieved in a coherent communication system using a true LO.