Continuous-variable quantum secure direct communication based on N-APSK with Boltzmann–Maxwell distribution

Continuous-variable quantum secure direct communication (CVQSDC) with Gaussian modulation (GM) demands a considerable quantity of random numbers during the preparation process and encodes them separately on the quadrature components of the quantum states. Hence, high-speed random number generators are required to satisfy this demand, which is difficult to implement in practical applications. CVQSDC with discrete modulation (DM), correspondingly, employs a finite number of quantum states to achieve encoding, which can circumvent the shortcomings of the GM scheme. Based on the advantages of DM, the issue of attaining the most optimal secrecy capacity and communication distance remains to be resolved. Here, we propose a CVQSDC protocol based on N-symbol amplitude phase shift keying (N-APSK), which exploits the Boltzmann–Maxwell distribution assisted probability shaping technique. In comparison with the uniform distribution, according to 32-APSK CVQSDC, the proposed scheme extends the communication distance by about 38%, while obtaining a higher secrecy capacity at the same communication distance. Furthermore, increasing the value of N will concurrently increase the quantity of rings in the constellation, thereby facilitating enhancements of communication distance. This work incorporates the modulation approaches prevalently employed in classical communication into the realm of quantum communication, attaining gratifying advancements in communication distance and secrecy capacity, and concurrently facilitating the integrated development of quantum communication and classical communication.