Toward practical quantum encryption in phase space: simulated QPSK and 16-QAM with dynamic displacement operators

Building upon the theoretical framework of Dynamic Displacement Operators (DDO) introduced in Ref. (Kuang, in Acad Quantum 2, 2025, https://doi.org/10.20935/AcadQuant7462), we present a simulation validation of a quantum-enhanced encryption scheme for coherent optical communication systems in phase space. The method integrates random phase shift operators (PSOs) and displacement operators (DOs) to dynamically manipulate information symbols on a symbol-by-symbol basis, enabling secure physical-layer encryption. Simulation results confirm that accurate decryption is only possible with the correct operator pair; any mismatch in displacement or phase parameters leads to bit error rates approaching 50%, effectively blocking unauthorized access. We further compare the performance of unencrypted transmission with various quantum-enhanced physical-layer security (QEPS) configurations over different fiber lengths, and explicitly validate the scalability of the proposed scheme by simulating a higher-order Quantum Permutation Pad (QPP) with a depth of $m = 2$ for 16-QAM. The results validate the robustness of the proposed DDO-based scheme against partial or incorrect decryption attempts, underscoring its potential for securing data transmission in classical optical networks.