Quantum encryption in phase space with dynamic displacement operators and quantum permutation pad
Randy Kuang · Academia quantum. · 2025
We propose the Dynamic Displacement Operator (DDO) as part of Quantum Encryption in Phase Space (QEPS-dd), a novel scheme for securing coherent optical communications using Quadrature Amplitude Modulation (QAM). In this framework, the K-QAM encoding is modeled as a quantum operator, with its constellation points forming the eigenbasis. The encoding and decoding processes are treated as operations of this quantum operator on its eigenstates, ensuring coherent communication via digital signal processing at both the transmission and reception sides. The DDO combines a displacement operator and a phase-shift operator, producing dynamic effects that enhance the randomization of the cipher constellation, thus significantly improving communication security. To further strengthen encryption, we introduce the Quantum Permutation Pad (QPP), which randomizes the DDO basis. Together, these components offer robust protection against both classical and quantum attacks. Our security analysis shows that the most effective attack is a brute-force search for the secret DDO pad, with a computational complexity of Ο(2ℓ!), where ℓ represents the bit length of the DDO pad. As ℓ increases, the factorial growth in complexity makes the system resistant to classical methods and quantum algorithms such as Grover’s search. Building on prior experimental results with phase-shift (QEPS-p) and displacement (QEPS-d) operators, we propose that QEPS-dd can be implemented for high-speed quantum-secure communication over existing optical networks, offering a practical solution for enhancing communication security.