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Communications Physics

Pilot reference free continuous variable quantum key distribution with amplitude encoding

Mingxuan Guo, Peng Huang, Bangde Zhu, Kuntuo Zhu, Tao Wang, Guihua Zeng

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CVQKD) serves as a vital tool for safeguarding information security. Currently, CVQKD is primarily implemented using a local oscillator. This scheme requires transmitting a high-energy pilot signal as a reference to correct phase drift. However, the pilot signal introduces crosstalk into the quantum signal and complicates digital signal processing. Here we show a pilot-reference-free CVQKD protocol with a local oscillator, where the secret key is encoded on the amplitude of coherent states. The protocol does not require a pilot signal, eliminating pilot-induced crosstalk. We conduct security analysis under collective attacks and simulate its secret key rate. Finally, we perform a proof-of-principle experiment under an optical fiber channel and a free-space channel containing biaxially oriented polypropylene, where the phase of the signal is fully randomized. The protocol remains operable under randomized phase and simplifies physical implementation and digital signal processing, while adapting to optical path fluctuations in complex channels. Continuous variable quantum key distribution with local oscillators typically requires pilot signals to track phase drift. Here, the authors show how to extract keys from signal amplitudes, enabling pilot free operation and proof of principle key generation even when the optical phase is randomised.

DOI
10.1038/s42005-026-02842-x

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Continuous-variable quantum key distribution (CVQKD) serves as a vital tool for safeguarding information security. Currently, CVQKD is primarily implemented using a local oscillator. This scheme requires transmitting a high-energy pilot signal as a reference to correct phase drift. However, the pilot signal introduces crosstalk into the quantum signal and complicates digital signal processing. Here we show a pilot-reference-free CVQKD protocol with a local oscillator, where the secret key is encoded on the amplitude of coherent states. The protocol does not require a pilot signal, eliminating pilot-induced crosstalk. We conduct security analysis under collective attacks and simulate its secret key rate. Finally, we perform a proof-of-principle experiment under an optical fiber channel and a free-space channel containing biaxially oriented polypropylene, where the phase of the signal is fully randomized. The protocol remains operable under randomized phase and simplifies physical implementation and digital signal processing, while adapting to optical path fluctuations in complex channels. Continuous variable quantum key distribution with local oscillators typically requires pilot signals to track phase drift. Here, the authors show how to extract keys from signal amplitudes, enabling pilot free operation and proof of principle key generation even when the optical phase is randomised.
A high-speed Gaussian-modulated continuous-variable quantum key distribution (CVQKD) with a local local oscillator (LLO) is experimentally demonstrated based on pilot-tone-assisted phase compensation. In the proposed scheme, the frequency-multiplexing and polarization-multiplexing techniques are used for the separate transmission and heterodyne detection between quantum signal and pilot tone, guaranteeing no crosstalk from strong pilot tone to weak quantum signal and different detection requirements of low-noise for quantum signal and high-saturation limitation for pilot tone. Moreover, compared with the conventional CVQKD based on homodyne detection, the proposed LLO-CVQKD scheme can measure X and P quadrature simultaneously using heterodyne detection without need of extra random basis selection. Besides, the phase noise, which contains the fast-drift phase noise due to the relative phase of two independent lasers and the slow-drift phase noise introduced by quantum channel disturbance, has been compensated experimentally in real time, so that a low level of excess noise with a 25 km optical fiber channel (with 5 dB loss) is obtained for the achievable secure key rate of 7.04 Mbps in the asymptotic regime and 1.85 Mbps under the finite-size block of 107.
We propose a pilot-multiplexed continuous-variable quantum key distribution (CVQKD) scheme based on a local local oscillator (LLO). Our scheme utilizes time-multiplexing and polarization-multiplexing techniques to dramatically isolate the quantum signal from the pilot, employs two heterodyne detectors to separately detect the signal and the pilot, and adopts a phase compensation method to almost eliminate the multifrequency phase jitter. In order to analyze the performance of our scheme, a general LLO noise model is constructed. Besides the phase noise and the modulation noise, the photon-leakage noise from the reference path and the quantization noise due to the analog-to-digital converter (ADC) are also considered, which are first analyzed in the LLO regime. Under such general noise model, our scheme has a higher key rate and longer secure distance compared with the preexisting LLO schemes. Moreover, we also conduct an experiment to verify our pilot-multiplexed scheme. Results show that it maintains a low level of the phase noise and is expected to obtain a 554-Kbps secure key rate within a 15-km distance under the finite-size effect.
A significant performance inhibitor of free-space continuous variable quantum key distribution (CVQKD) is turbulence, which gives rise to wavefront phase and amplitude aberrations. We demonstrate that in a turbulent channel, during coherent state transmissions from a continuous-wave laser, that the interferometric visibility between the local oscillator (LO) and quantum signal decreases. A solution to this is incorporating adaptive optics at the receiver to correct phase and amplitude aberrations in the wavefronts of the received quantum signal. We demonstrate the increased interferometric visibility and decrease in its fluctuations in a 60 cm and 30 m turbulent channel when using adaptive optics through channel characterisation. In an ideal CVQKD system, we show that this leads to more precise and larger positive secret key rates, improving the performance of free-space CVQKD in turbulent channels.
A significant performance inhibitor of free-space continuous variable quantum key distribution (CVQKD) is turbulence, which gives rise to wavefront phase and amplitude aberrations. We demonstrate that in a turbulent channel, during coherent state transmissions from a continuous-wave laser, that the interferometric visibility between the local oscillator (LO) and quantum signal decreases. A solution to this is incorporating adaptive optics at the receiver to correct phase and amplitude aberrations in the wavefronts of the received quantum signal. We demonstrate the increased interferometric visibility and decrease in its fluctuations in a 60 cm and 30 m turbulent channel when using adaptive optics through channel characterisation. In an ideal CVQKD system, we show that this leads to more precise and larger positive secret key rates, improving the performance of free-space CVQKD in turbulent channels.
We experimentally demonstrate a 25 MHz repetition rate pilot-tone-assisted Gaussian-modulated continuous-variable quantum key distribution (CVQKD) with a local local oscillator (LLO) by employing the frequency-multiplexing and polarization-multiplexing techniques. In the proposed LLO-CVQKD system, the strong pilot tone and weak quantum signal can be separated in different frequency and polarization domain for avoiding the crosstalk between them and guaranteeing different detection requirements of low-noise for quantum signal and high-saturation limitation for pilot tone. Moreover, the dominant phase noise over 25 km optical fiber channel can be compensated in real time for supporting high secure key rate of 1.61 Mbps in the asymptotic regime.
Local local oscillator (LLO) continuous-variable quantum key distribution (CVQKD) schemes have been extensively studied for their enhanced security and simplified system implementation. However, such schemes typically require numerous pilot signals to compensate for phase drift caused by two independent lasers, which significantly increases system overhead and limits the achievable secret key rate. In this work, we propose an enhanced-rate CVQKD scheme, which aims to enhance the secret key rate by achieving high-accuracy phase compensation based on a particle filter (PF) algorithm under low system overhead. Specifically, to counter the loss in phase estimation accuracy due to the reduced number of pilot signals, we introduce a PF-based carrier phase recovery algorithm, complemented by an exponentially weighted phase prediction method to improve phase estimation accuracy. This approach effectively suppresses excess noise under limited pilot information and improves phase compensation precision. Experimental results demonstrate that, compared to the traditional scheme with a 1:1 signal-to-pilot number ratio, our method achieves its maximum performance with a signal-to-pilot number ratio of 3:1, while maintaining phase compensation accuracy virtually unchanged, reducing system overhead by 50% and achieving a 147% improvement in the secret key rate, reaching 235 kbps in a 30 km standard fiber link.