https://doi.org/10.1140/epjqt/s40507-026-00480-4
Research
Toward practical quantum encryption in phase space: simulated QPSK and 16-QAM with dynamic displacement operators
1
Information Support Force Engineering University, 450007, Wuhan, China
2
Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, 530004, Nanning, China
3
Research, Quantropi Inc., 1545 Carling Av, Suite 620, K1Z 8P9, Ottawa, ON, Canada
a
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b
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Received:
11
July
2025
Accepted:
11
February
2026
Published online:
27
February
2026
Abstract
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 
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.
Key words: Quantum encryption / Coherent optical communication / Dynamic displacement operator (DDO) / Physical-layer security / Phase space modulation / Bit error rate (BER) / Quantum-enhanced physical security (QEPS) / Displacement operator / Phase shift operator / Quantum Permutation Pad (QPP)
© The Author(s) 2026
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