© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Nanosystems Physics Chemistry Mathematics

Heterodyne detection method of multimode states for subcarrier wave continuous variable quantum key distribution

I. M. Filipov, R. Goncharov, Michael V. Dashkov, Ekaterina I. Bogdanova, A.V. Zinovev, Vladimir Chistiakov, Fedor Dmitrievich Kiselev

Published Jan 6, 2026• 0 citations

Abstract

A novel coherent detection method for subcarrier wave (SCW) quantum states applied to continuousvariable quantum key distribution (CV-QKD) is presented. The proposed approach relies on repeated phase modulation at the receiver and spatial separation of the carrier and subcarrier frequency components. The resulting output is an intermediate frequency determined by the difference between the sender’s and receiver’s modulation frequencies. An analytical model of the detection output is developed through time-varying modulation using a classical method based on Bessel functions, and a comparative analysis with alternative heterodyne detection methods is provided. Experimental validation confirms the linear dependence of the output signal on the receiver’s modulation frequency and the sender’s modulation index in the small-modulation regime. Furthermore, the feasibility of the proposed method is demonstrated through the detection of discretely modulated signals using quadrature phase-shift keying (QPSK).

DOI: 10.17586/2220-8054-2025-16-6-778-784

Related papers

Coherent detection schemes for subcarrier wave continuous variable quantum key distribution

E.O. Samsonov, R. Goncharov, M.A. Fadeev +5 more

We examine different methods to implement coherent detection in subcarrier wave quantum key distribution (SCW QKD) systems. For classical wave fields, we present the models describing homodyne-type and heterodyne-type coherent detection schemes needed to extract information from the quadrature phase-coded multimode signals used in SCW QKD. Practical feasibility of the proposed schemes is corroborated by experiments.

arXiv:2006.16543•Journal of the Optical Society of America B•Jun 11, 2021•16 citations

Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis

E.O. Samsonov, R. Goncharov, Andrei Gaidash +3 more

In this paper we report a continuous-variable quantum key distribution protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. We propose a coherent detection scheme where power from a carrier wave is used as a local oscillator. We compose a mathematical model of the proposed scheme and perform its security analysis in the finite-size regime using fully quantum asymptotic equipartition property technique. We calculate a lower bound on the secret key rate for the system under the assumption that the quantum channel noise is negligible compared to detector dark counts, and an eavesdropper is restricted to collective attacks. Our calculation shows that the current realistic system implementation would allow distributing secret keys over channels with losses up to 9 dB.

arXiv:1910.04431•Scientific Reports•Jun 22, 2020•37 citations

Phase estimation using homodyne detection for continuous variable quantum key distribution

Mi Zou, Yingqiu Mao, Teng‐Yun Chen

In order to ensure the security of the local oscillator (LO) in continuous variable quantum key distribution (CV-QKD), the LO in CV-QKD based on the local LO (LLO) scheme no longer passes through the quantum channel. For the LLO scheme using homodyne detection, two orthogonal quadratures of reference pulse can only be measured sequentially, which, as a result, each signal pulse should be accompanied by a pair of identical reference pulses. However, due to the phase shift between two adjacent pulses, it is difficult to prepare dual reference pulses with the same phase relative to the LO. In this paper, we propose an improved method to get around this difficulty, which is demonstrated experimentally for a transmitter and a receiver connected by a 50 km single mode fiber. The phase noise measured in the experiment is 2.0×10−3rad2, which is comparable to the recent experimental results using heterodyne detection. This method simplifies the preparation of phase reference pulses and removes the obstacles for the application of homodyne detection in the LLO scheme. In addition, this method can also be used for the compensation of quadrature imbalance in heterodyne detection, then the performance of heterodyne detection can be improved.

Journal of Applied Physics•Aug 9, 2019•6 citations

Solution of the Convex Optimization Problem for Subcarrier Wave Continuous-Variable Quantum Key Distribution Protocol with Discrete Modulation

N. Ivankov, R. Goncharov, D. V. Tupyakov

This paper introduces an approach to solving the convex optimization problem for subcarrier wave continuous-variable quantum key distribution (QKD) protocol using discrete modulation. For the first time, we provide a solution to this problem. By employing semidefinite programming, we have estimated the lower bound of the secure key generation rate in the asymptotic limit, taking into account an optimal attack from potential eavesdroppers. We considered an optical scheme that involves the use of quadrature phase modulation of coherent states and coherent detection based on the interference between the carrier and side frequencies. Our findings demonstrate the feasibility of distributing secure key generation rates over distances exceeding 100 km, even in the presence of realistic excess noise.

Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)•May 29, 2023•0 citations

Subcarrier wave continuous-variable quantum key distribution with Gaussian modulation: composable security analysis

R. Goncharov, Alexei D. Kiselev, E.O. Samsonov +1 more

In this paper, we continue the study of the quantum cryptographic GG02 protocol, performed using the approach based on the subcarrier waves. We modify the scheme via heterodyne detection and perform security analysis for the full trusted hardware noise model in the presence of collective attacks with finite-key effects. It is shown that the system can potentially distribute the key even if the level of losses in the channel is above 9 dB. This result is consistent with the general technical level and comply with modern standards of practical CV-QKD systems. Finally, the system under consideration fully meets the criterion of composability.

Computer Optics•Apr 24, 2023•10 citations

Satellite-based Free-Space Quantum Key Distribution Systems using QPSK Modulation and Heterodyne Detection Receiver

Minh B. Vu, Hien T. T. Pham, Trung-Anh Do +2 more

This paper proposes to design a satellite-based free-space quantum key distribution (QKD) systems using quadrature phase-shift-keying (QPSK) signaling. Our proposed QKD system based on continuous variable encoding to provide the secret-key transmission, where the key information is encoded on four coherent states corresponding to QPSK modulation scheme. In addition, we use heterodyne detection receiver to improve the receiver sensitivity thus decode the signal with high fidelity. The performance of the proposed free-space QKD system is analytically investigated. More especially, the mathematical expression for quantum bit error rate (QBER) is derived taking into account the effect of physical layer impairments and parameters. The numerical results help to determine the appropriate values of system's parameters such as the threshold coefficients and the required transmitted power.

International Symposium on Communications and Information Technologies•Sep 1, 2019•10 citations

A novel coherent detection method for subcarrier wave (SCW) quantum states applied to continuousvariable quantum key distribution (CV-QKD) is presented. The proposed approach relies on repeated phase modulation at the receiver and spatial separation of the carrier and subcarrier frequency components. The resulting output is an intermediate frequency determined by the difference between the sender’s and receiver’s modulation frequencies. An analytical model of the detection output is developed through time-varying modulation using a classical method based on Bessel functions, and a comparative analysis with alternative heterodyne detection methods is provided. Experimental validation confirms the linear dependence of the output signal on the receiver’s modulation frequency and the sender’s modulation index in the small-modulation regime. Furthermore, the feasibility of the proposed method is demonstrated through the detection of discretely modulated signals using quadrature phase-shift keying (QPSK).

In this paper we report a continuous-variable quantum key distribution protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. We propose a coherent detection scheme where power from a carrier wave is used as a local oscillator. We compose a mathematical model of the proposed scheme and perform its security analysis in the finite-size regime using fully quantum asymptotic equipartition property technique. We calculate a lower bound on the secret key rate for the system under the assumption that the quantum channel noise is negligible compared to detector dark counts, and an eavesdropper is restricted to collective attacks. Our calculation shows that the current realistic system implementation would allow distributing secret keys over channels with losses up to 9 dB.

In order to ensure the security of the local oscillator (LO) in continuous variable quantum key distribution (CV-QKD), the LO in CV-QKD based on the local LO (LLO) scheme no longer passes through the quantum channel. For the LLO scheme using homodyne detection, two orthogonal quadratures of reference pulse can only be measured sequentially, which, as a result, each signal pulse should be accompanied by a pair of identical reference pulses. However, due to the phase shift between two adjacent pulses, it is difficult to prepare dual reference pulses with the same phase relative to the LO. In this paper, we propose an improved method to get around this difficulty, which is demonstrated experimentally for a transmitter and a receiver connected by a 50 km single mode fiber. The phase noise measured in the experiment is 2.0×10−3rad2, which is comparable to the recent experimental results using heterodyne detection. This method simplifies the preparation of phase reference pulses and removes the obstacles for the application of homodyne detection in the LLO scheme. In addition, this method can also be used for the compensation of quadrature imbalance in heterodyne detection, then the performance of heterodyne detection can be improved.

This paper introduces an approach to solving the convex optimization problem for subcarrier wave continuous-variable quantum key distribution (QKD) protocol using discrete modulation. For the first time, we provide a solution to this problem. By employing semidefinite programming, we have estimated the lower bound of the secure key generation rate in the asymptotic limit, taking into account an optimal attack from potential eavesdroppers. We considered an optical scheme that involves the use of quadrature phase modulation of coherent states and coherent detection based on the interference between the carrier and side frequencies. Our findings demonstrate the feasibility of distributing secure key generation rates over distances exceeding 100 km, even in the presence of realistic excess noise.

In this paper, we continue the study of the quantum cryptographic GG02 protocol, performed using the approach based on the subcarrier waves. We modify the scheme via heterodyne detection and perform security analysis for the full trusted hardware noise model in the presence of collective attacks with finite-key effects. It is shown that the system can potentially distribute the key even if the level of losses in the channel is above 9 dB. This result is consistent with the general technical level and comply with modern standards of practical CV-QKD systems. Finally, the system under consideration fully meets the criterion of composability.

This paper proposes to design a satellite-based free-space quantum key distribution (QKD) systems using quadrature phase-shift-keying (QPSK) signaling. Our proposed QKD system based on continuous variable encoding to provide the secret-key transmission, where the key information is encoded on four coherent states corresponding to QPSK modulation scheme. In addition, we use heterodyne detection receiver to improve the receiver sensitivity thus decode the signal with high fidelity. The performance of the proposed free-space QKD system is analytically investigated. More especially, the mathematical expression for quantum bit error rate (QBER) is derived taking into account the effect of physical layer impairments and parameters. The numerical results help to determine the appropriate values of system's parameters such as the threshold coefficients and the required transmitted power.