Quantum Encryption in Phase Space using Displacement Operator for QPSK Data Modulation

Quantum Public Key Distribution or QPKE with the randomized phase shift gate was proposed by Kuang and Bettenburg in 2020. It has been implemented theoretically with simulations and experimentally over existing fiber optical networks since then. QPKE can be considered as an RSA-type scheme in optical analogue domain. QPKE was renamed as Quantum Encryption in Phase Space or QEPS to reflect the encryption of coherent states in phase space. QEPS with the phase shift gate can only be applied to data modulation scheme with phase shift keying such as quadrature phase shift keying or QPSK. It would leak data information in amplitude once it is applied to quadrature amplitude modulation or QAM schemes. Kuang and Chan recently proposed a new version of QEPS called Quantum Encryption in Phase Space with the displacement gate or QEPS-d. It demonstrated to overcome the limitation of QEPS with the phase shift gate. We introduced a reduced displacement operator by ignoring the global phase factor then the reduced displacement operators are commutable. This commutability helps our implementation at both transmission and receiving. An arbitrary displacement operator can be decoupled into a standard QAM modulation with a phase shift modulation to ease our encryption and decryption. This paper simulates the QEPS-d encryption for QPSK data modulation to demonstrate how QEPS-d works.