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Science China Information Sciences

Reverse-encoded quantum key distribution with Gaussian-modulated coherent states

Mingxuan Guo, Peng Huang, Tao Wang, Guihua Zeng

Published Mar 3, 2026• 1 citation
Publisher
DOI
10.1007/s11432-025-4575-5

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A novel quantum key distribution (QKD) protocol is proposed and demonstrated. It is based on the transmission of Gaussian-modulated coherent states that are laser pulses containing a few hundred photons .Shot-noise limited coherent (homodyne) detection is used, which makes it possible to achieve high secret-key rates. It remains, in principle, efficient for any value of the line transmission by use of a "reverse reconciliation" technique, which is shown to be secure against individual attacks based on entanglement and quantum memories. The basic idea is to use a reverse reconciliation protocol, that is, Alice attempts to guess what was received by Bob rather than Bob guessing what was sent by Alice. A reverse protocol always gives Alice an advantage over a potential eavesdropper Eve, regardless the line loss. In addition, a specific advantage of using quantum continuous variables is that the high dimensionality of the phase space may be exploited by modulating the field quadratures with a large dynamics, allowing the encoding of several key bits per pulse. This, together with the fact that fast modulation and detection can be achieved, results in a high-rate secret key distribution.
Discrete-modulated coherent-state continuous-variable quantum key distribution (DMCS-CVQKD) is of great value for its simple implementation. However, the traditional DMCS-CVQKD scheme cannot tolerate the high channel excess noise and channel loss, compared to the Gaussian-modulated scheme, and its error correction is still difficult. In this paper, we propose a discrete-modulated coherent-state basis-encoding quantum key distribution (DMCS-BE-QKD) protocol, where the secret keys are encoded in the random choice of 2 measurement bases, i.e., the conjugate quadratures X and P of discrete-modulated coherent states, and it only needs simple binary sequence error correction. We analyze the secret key rate of DMCS-BE-QKD protocol under individual and collective attacks in the linear Gaussian channel. The results show that DMCS-BE-QKD can greatly enhance the ability to tolerate the channel loss and excess noise compared to the original DMCS-CVQKD protocol, which can tolerate approximately 40 dB more channel loss compared to the original DMCS-CVQKD for the realistic value of noise. Finally, a proof-of-principle experiment is conducted under a 50.5-km optical fiber to verify the feasibility of DMCS-BE-QKD. It is based on the consistent physical procedures of the traditional DMCS-CVQKD, which makes it perfectly compatible to deployed terminals and can serve as a multiplier for the practical secure quantum cryptography communication in harsh environments.