In 2020, Kuang and Bettenburg proposed Quantum Public Key Envelope (QPKE) which utilized the randomized phase shift gate. Since then, it has been implemented both theoretically through simulations and experimentally over existing fiber optical networks. QPKE can be compared to an RSA-type scheme but in the optical analogue domain. Later, it was renamed Quantum Encryption in Phase Space (QEPS) to emphasize the encryption of coherent states in phase space. However, the phase shift gate used in QEPS is limited to data modulation schemes with phase shift keying such as quadrature phase shift keying (QPSK) as it may leak data information in amplitude if applied to quadrature amplitude modulation (QAM) schemes. Recently, Kuang and Chan proposed a new version of QEPS known as Quantum Encryption in Phase Space with the displacement gate or QEPS-d, which overcomes the limitation of QEPS with the phase shift gate. This was achieved by introducing a reduced displacement operator that ignores the global phase factor, making the reduced displacement operators commutable, thus aiding the implementation at both transmission and reception. Furthermore, any arbitrary displacement operator can be decoupled into a standard QAM modulation with a phase shift modulation, making encryption and decryption easier. This paper demonstrates the simulation of QEPS-d encryption for QPSK data modulation to illustrate how QEPS-d functions.
In 2020, Kuang and Bettenburg proposed Quantum Public Key Envelope (QPKE) which utilized the randomized phase shift gate. Since then, it has been implemented both theoretically through simulations and experimentally over existing fiber optical networks. QPKE can be compared to an RSA-type scheme but in the optical analogue domain. Later, it was renamed Quantum Encryption in Phase Space (QEPS) to emphasize the encryption of coherent states in phase space. However, the phase shift gate used in QEPS is limited to data modulation schemes with phase shift keying such as quadrature phase shift keying (QPSK) as it may leak data information in amplitude if applied to quadrature amplitude modulation (QAM) schemes. Recently, Kuang and Chan proposed a new version of QEPS known as Quantum Encryption in Phase Space with the displacement gate or QEPS-d, which overcomes the limitation of QEPS with the phase shift gate. This was achieved by introducing a reduced displacement operator that ignores the global phase factor, making the reduced displacement operators commutable, thus aiding the implementation at both transmission and reception. Furthermore, any arbitrary displacement operator can be decoupled into a standard QAM modulation with a phase shift modulation, making encryption and decryption easier. This paper demonstrates the simulation of QEPS-d encryption for QPSK data modulation to illustrate how QEPS-d functions.
In 2020, Kuang and Bettenburg proposed Quantum Public Key Distribution (QPKE) which utilized the randomized phase shift gate. Since then, it has been implemented both theoretically through simulations and experimentally over existing fiber optical networks. QPKE can be compared to an RSA-type scheme but in the optical analogue domain. Later on, it was renamed Quantum Encryption in Phase Space (QEPS) to emphasize the encryption of coherent states in phase space. However, the phase shift gate used in QEPS is limited to data modulation schemes with phase shift keying such as quadrature phase shift keying (QPSK) as it may leak data information in amplitude if applied to quadrature amplitude modulation (QAM) schemes. Recently, Kuang and Chan proposed a new version of QEPS known as Quantum Encryption in Phase Space with the displacement gate or QEPS-d, which overcomes the limitation of QEPS with the phase shift gate. This was achieved by introducing a reduced displacement operator that ignores the global phase factor, making the reduced displacement operators commutable, thus aiding the implementation at both transmission and reception. Furthermore, any arbitrary displacement operator can be decoupled into a standard QAM modulation with a phase shift modulation, making encryption and decryption easier. This paper demonstrates the simulation of QEPS-d encryption for QPSK data modulation to illustrate how QEPS-d functions.
Abstract 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.
Quantum Encryption in Phase Space (QEPS) is a physical-layer encryption framework that harnesses the quantum-mechanical properties of coherent states to secure optical communications against both classical and quantum computational threats. By applying randomized phase shifts, displacements, or their dynamic combinations—implemented as unitary transformations in phase space—QEPS disrupts the phase reference essential for coherent detection, establishing aphase synchronization barrier. This review synthesizes the theoretical foundations, security mechanisms, and experimental progress of the QEPS framework, encompassing its three principal variants: the round-trip Quantum Public Key Envelope (QPKE) protocol—a public-key-like scheme built upon phase randomization (QEPS-p), the symmetric phase-only QEPS-p, and the displacement-based QEPS-d. Experimental validations demonstrate that authorized users achieve bit-error rates (BERs) below the forward-error-correction threshold, whereas eavesdroppers are confined to BERs near 50%, equivalent to random guessing—all while utilizing standard coherent optical transceivers at data rates up to 200 Gb/s over 80 km of fiber. We further examine QEPS’s robustness to channel impairments, its seamless compatibility with existing digital signal processing (DSP) pipelines, and its distinctive position within the post-quantum cryptography landscape. Finally, we outline key challenges and future research directions toward deploying QEPS as a practical, quantum-resistant security layer for next-generation optical networks.
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.
Abstract We propose and simulate a quantum-enhanced encryption scheme for coherentoptical communication systems based on coherent-state dynamic displacementoperators (DDOs) in phase space. The method integrates random phase shiftoperators (PSOs) and displacement operators (DOs) to dynamically manipu-late information symbols, enabling secure physical-layer encryption. Simulationresults confirm that accurate decryption is only possible with the correct operatorpair; any mismatch in displacement or phase parameters leads to bit error ratesapproaching 50%, effectively blocking unauthorized access. We further comparethe performance of unencrypted transmission with various quantum-enhancedphysical-layer security (QEPS) configurations over different fiber lengths. Theresults validate the robustness of the proposed DDO-based scheme against par-tial or incorrect decryption attempts, underscoring its potential for securing datatransmission in classical optical networks.
Optical layer attacks on communication networks are one of the weakest reinforced areas of the network, allowing attackers to overcome security when proper safeguards are not put into place. Here, we present our solution or Quantum Encryption in Phase Space (QEPS), a physical layer encryption method to secure data over the optical fiber, based on our novel round-trip Coherent-based Two-Field Quantum Key Distribution (CTF-QKD) scheme. We perform a theoretical study through simulation and provide an experimental demonstration. The same encryption is used for QEPS as CTF-QKD but achieved through a pre-shared key and one-directional transmission design. QEPS is uniquely different from traditional technology where encryption is performed at the optical domain with coherent states by applying a quantum phase-shifting operator. The pre-shared secret is used to seed a deterministic random number generator and control the phase modulator at the transmitter for encryption and at the receiver for decryption. Using commercially available simulation software, we study two preventative measures for different modulation formats which will prevent an eavesdropper from obtaining any data. QEPS demonstrates that it is secure against tapping attacks when attackers have no information of the phase modulator and pre-shared key. Finally, an experiment with commercial components demonstrates QEPS system integrability.