In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced at the receiver side to reduce the impact of channel excess noise. Implemented by linear optical elements, homodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combining the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the secret key rate is closely related to the tuning gain and the transmittance of LOCM. Once the two parameters are set to appropriate values, LOCM allows the promotion of the secret key rate of DPM-CVQKD, as well as its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Since the performance of LOCM DPM-CVQKD is heavily reliant on the calibrate selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be exploited.
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