Quantum encryption in phase space with displacement operators

In photonic computing, the quantum systems consist of coherent states and squeezed coherent states. Common quantum gates found in these systems are: phase shift, displacement, and squeezing gates. These gates are all unitary and reversible. Outside of quantum systems, coherent states also plays a significant role in coherent optical communications with speeds of hundreds of gigabits per second. Secure optical communications is generally implemented at the data layer with classical symmetric encryption such as Advanced Standard Encryption or AES. This inevitably allows any wiretapping to capture the transmitted data either in the plaintext mode or in the encrypted ciphertext mode in the optical infrastructure. The recent and rapid developments in Quantum computing further lift up the need for quantum secure communications in the optical infrastructure. This paper proposes a novel quantum encryption in the coherent optical domain utilizing a displacement operator and implementing with IQ-MZM optical modules, called Quantum Encryption in Phase Space or QEPS. The communication peers share a secret used to seed cryptographic pseudo random number generators to produce a synchronized random number at both the transmitter and receiver. The synchronized random numbers are used to establish displacement operators to encrypt the coherent states at the transmission and decrypt the cipher coherent states at the receiver. Therefore, malicious parties tapping along the fibre line would not extract the message in transit from optical domain due to a high Bit Error Rate or BER. The optimal displacement operator is split into a standard 16-QAM and a random phase shift operator to enhance the transmission security. We analysis the transmission security with the wiretap channel model for semantic security. We have simulated the QEPS encryption and decryption for two data modulation schemes: QPSK and 16-QAM over 80 km for transmission speeds of 56 Gbps for QPSK and 112 Gbps for 16-QAM.