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Physical Review A

Intermode-interaction-induced dynamics of continuous-variable quantum-key-distribution observables

Andrei Gaidash, Alexei D. Kiselev, George P. Miroshnichenko, Козубов Антон Владимирович

Published Jun 21, 2024• 0 citations
Publisher

Abstract

We theoretically study the dynamical regimes of the observables that govern the operating conditions of continuous-variable (CV) quantum-key-distribution (QKD) systems, depending on quantum-channel-induced intermode interactions. In contrast to the widely used approach in which losses and thermal broadening are introduced through a beam-splitter transformation, our analysis uses the exactly solvable quantum channel model describing the Lindblad dynamics of multimode bosonic systems interacting with a heat bath and additionally takes into account imperfections of the homodyne-detection scheme. The analytical results for the photon-count difference and the quadrature probability distributions are used to derive the expression for the mutual information between legitimate parties, which explicitly links the information properties of CV QKD and the parameters of the channel. For the important special case of a two-mode photonic system propagating in a fiber channel, the latter can be conveniently parameterized using the frequency and the relaxation-rate vectors that characterize the coherent (dynamical) intermode couplings and the incoherent (environment mediated) interaction between the bosonic modes, respectively. It turns out that these vectors determine four qualitatively different dynamical regimes of the mutual information and the phase difference between the signal and the local oscillator that may significantly affect the operation of CV QKD.

DOI
10.1103/physreva.109.062615

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We theoretically study the dynamical regimes of the observables that govern the operating conditions of continuous-variable (CV) quantum-key-distribution (QKD) systems, depending on quantum-channel-induced intermode interactions. In contrast to the widely used approach in which losses and thermal broadening are introduced through a beam-splitter transformation, our analysis uses the exactly solvable quantum channel model describing the Lindblad dynamics of multimode bosonic systems interacting with a heat bath and additionally takes into account imperfections of the homodyne-detection scheme. The analytical results for the photon-count difference and the quadrature probability distributions are used to derive the expression for the mutual information between legitimate parties, which explicitly links the information properties of CV QKD and the parameters of the channel. For the important special case of a two-mode photonic system propagating in a fiber channel, the latter can be conveniently parameterized using the frequency and the relaxation-rate vectors that characterize the coherent (dynamical) intermode couplings and the incoherent (environment mediated) interaction between the bosonic modes, respectively. It turns out that these vectors determine four qualitatively different dynamical regimes of the mutual information and the phase difference between the signal and the local oscillator that may significantly affect the operation of CV QKD.
In continuous-variable quantum key distribution (CV-QKD), the key information are encoded on quadratures of the optical field, which are measured via balanced homodyne detector (BHD). The bandwidth of the BHD is one of key parameters for precise characterization of quantum states. We establish a theoretical model to analyze the impact of the BHD bandwidth and signal modulation patterns on the channel parameters estimation of CV-QKD systems. Based on the proposed model, the secure key rate of a practical CV-QKD system under different BHD bandwidths and signal modulation patterns are investigated. Our results show that insufficient BHD bandwidth will result in wrong estimate of the transmission loss and excess noise, which significantly affects the performance of CV-QKD systems. Given the BHD bandwidth, there exists an optimal signal repetition rate that maximizes the secure key rate. The BHD bandwidth requirement of the QKD system increases with the transmission distance for large duty cycle pulse. Furthermore, the root raised-cosine pulse signal modulation performs better than the square pulse signal modulation in general.
Quantum key distribution with continuous variables (CV-QKD) enables two parties to share a secret key by using coherent states of light and homodyne detection. This can be carried out by employing low-cost and mature technology developed for telecommunications. It has been shown that at short distances, CV-QKD allows for higher bit rates than conventional discrete variable QKD protocols. Furthermore, CV-QKD could potentially be employed to build a link for secure communication between two parties inside a building or campus and potentially in satellite communications. In this work, we will direct efforts into developing a fiber-based, low-cost, robust, and high-bitrate CV-QKD link. The theoretical concepts, specifics of the QKD system subsequently put into practice in the implementation, have been detailed. Finally, interference experiments have been performed parallel to the proof-of-principle QKD system.
In this paper, the crosstalk-induced impact of coexisting dense-wavelength-division-multiplexed (DWDM) channels on continuous-variable quantum key distribution (CV-QKD) in practical communication environment is investigated. We analyze the nonlinear effect resulting from classical channels on the transmitted local oscillator in CV-QKD, while various existing studies mainly focus on the crosstalk-induced excess noise. We demonstrate that the generally ignored phenomenon of four-wave mixing in excess noise analysis is a visible factor causing local oscillator fluctuation characterized by the statistical properties of the power evolution of local oscillator. Besides, the impact of stimulated Raman scattering on local oscillator is derived in the same theoretical approach and experimentally investigated. Finally, by establishing a trusted model for local oscillator fluctuation we perform the security analysis to constrain the threshold of fluctuation. All of the above analysis should be taken into account as a supplementary for evaluating the performance of CV-QKD with coexisting DWDM system and optimal allocation of classical and quantum channels.
Discrete-variable (DV) quantum key distribution (QKD) based on single-photon detectors and sources have been successfully deployed for long-range secure key distribution. On the other hand, continuous-variable (CV) quantum key distribution (QKD) based on coherent detectors and sources is currently lagging behind in terms of loss and noise tolerance. An important discerning factor between DV-QKD and CV-QKD is the effect of phase noise, which is known to be more relevant in CV-QKD. In this article, we investigate the effect of phase noise on DV-QKD and CV-QKD protocols, including the six-state protocol and squeezed-state protocol, in a thermal-loss channel but with the assumed availability of perfect sources and detectors. We find that in the low phase noise regime but high thermal noise regime, CV-QKD can tolerate more loss compared to DV-QKD. We also compare the secret key rate as an additional metric for the performance of QKD. Requirements for this quantity to be high vastly extend the regions at which CV-QKD performs better than DV-QKD. Our analysis addresses the questions of how phase noise affects DV-QKD and CV-QKD and why the former has historically performed better in a thermal-loss channel.
Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.
Quantum key distribution (QKD) enables two remote parties to share encryption keys with security based on the laws of physics. Continuous-variable (CV) QKD with coherent states and coherent detection integrates well with existing telecommunication networks. Thus far, long-distance CV-QKD has only been demonstrated using a highly complex scheme where the local oscillator is transmitted, opening security loopholes for eavesdroppers and limiting potential applications. Here, we report a long-distance CV-QKD experiment with a locally generated local oscillator over a 100-kilometer fiber channel with a total loss of 15.4 decibels. This record-breaking distance is achieved by controlling the phase noise-induced excess noise through a machine learning framework for carrier recovery and optimizing the modulation variance. We implement the full CV-QKD protocol and demonstrate the generation of keys secure against collective attacks in the finite-size regime. Our results mark a substantial milestone for realizing CV quantum access networks with a high loss budget and pave the way for large-scale deployment of secure QKD.