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Academia quantum.

Robust simulation of continuous-variable quantum key distribution in Matlab and Simulink

Shashank Gupta, Abhishek Mani Shukla, Arijit Roy, Sruthi Chennuri, Vijayalaxmi Mogligidda, Rajesh Kumar Krishnan, Dilip Singh

Published Aug 14, 2025• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution with coherent detection is widely acknowledged for its compatibility with contemporary optical communication technologies. However, the robustness of various modulation formats and detection procedures against high excess noise remains uncertain, posing a significant barrier to the widespread implementation of quantum key distribution networks. This paper introduces a Matlab and Simulink-based experimental simulator designed to analyze different modulation formats (Gaussian and discrete) and coherent detection techniques (homodyne, heterodyne, and intradyne). Our findings suggest that polarization-multiplexed quantum signals with discrete modulation and pilot tones exhibit greater resilience to experimental imperfections. Enhanced robustness can be achieved through post-selection. Furthermore, under conditions of trusted detector noise, intradyne detection proves more effective in mitigating various offsets between the two nodes, thereby resulting in an increased secret key rate. The secure key rate is determined using the Gaussian extremity theorem for Gaussian modulation and a strict numerical technique against collective attacks in the asymptotic regime for discrete modulation. The results demonstrate that the protocol enables key distribution over distances approaching intercity scales, thereby supporting the advancement of cost-effective quantum-secure communication networks.

DOI
10.20935/acadquant7844

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Continuous-variable quantum key distribution with coherent detection is widely acknowledged for its compatibility with contemporary optical communication technologies. However, the robustness of various modulation formats and detection procedures against high excess noise remains uncertain, posing a significant barrier to the widespread implementation of quantum key distribution networks. This paper introduces a Matlab and Simulink-based experimental simulator designed to analyze different modulation formats (Gaussian and discrete) and coherent detection techniques (homodyne, heterodyne, and intradyne). Our findings suggest that polarization-multiplexed quantum signals with discrete modulation and pilot tones exhibit greater resilience to experimental imperfections. Enhanced robustness can be achieved through post-selection. Furthermore, under conditions of trusted detector noise, intradyne detection proves more effective in mitigating various offsets between the two nodes, thereby resulting in an increased secret key rate. The secure key rate is determined using the Gaussian extremity theorem for Gaussian modulation and a strict numerical technique against collective attacks in the asymptotic regime for discrete modulation. The results demonstrate that the protocol enables key distribution over distances approaching intercity scales, thereby supporting the advancement of cost-effective quantum-secure communication networks.
Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices.However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks.In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying technique.By limiting information leakage, our proposed protocol enhances excess noise tolerance to a high level.Furthermore, we demonstrate that homodyne detection performs better than heterodyne detection in quaternary-modulated continuous-variable quantum key distribution under the untrusted detector noise scenario.The security is analyzed using the tight numerical method against collective attacks in the asymptotic regime.Our results imply that the current protocol can distribute keys in nearly intercity area and, thus, paves the way for constructing low-cost quantum secure communication networks.
Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of 0.1 − 10 − 4 bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of 10 Gbits of secret key after n ∼ 10 11 rounds and distances of few tens of kilometres.
Summary form only given. Continuous-variable quantum key distribution (CVQKD) is a promising alternative to commonly used discrete-variable QKD protocols, because this technology can be implemented with standard telecom components and recent results suggest that it will be compatible with standard wavelength division multiplexed telecommunication networks [1]. Security proofs against general eavesdropping attacks are available for CVQKD protocols using Gaussian modulation [2], and field implementations over deployed telecommunication networks have been demonstrated over the past few years [3].Long-distance operation of CVQKD systems, however, has been hindered until now by the limited efficiency of the complex error-correction (or reconciliation) algorithms that are required to extract the secret key from the correlated data shared by Alice and Bob. We have designed high-efficiency error correcting-codes [4] allowing to extract an errorless secret key in a CVQKD protocol using a Gaussian modulation of coherent states and a homodyne detection system. These codes are available for a wide range of signal-to-noise ratios on a Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method [5]. This improved reconciliation procedure considerably extends the secure range of a continuous-variable quantum key distribution with Gaussian modulation.
Continuous Variable (CV) quantum key distribution (QKD) is a promising candidate for practical implementations due to its compatibility with the existing communication technology. A trusted device scenario assuming that an adversary has no access to imperfections such as electronic noises in the detector is expected to provide significant improvement in the key rate, but such an endeavor so far was made separately for specific protocols and for specific proof techniques. Here, we develop a simple and general treatment that can incorporate the effects of Gaussian trusted noises for any protocol that uses homodyne/heterodyne measurements. In our method, a rescaling of the outcome of a noisy homodyne/heterodyne detector renders it equivalent to the outcome of a noiseless detector with a tiny additional loss, thanks to a noise-loss equivalence well-known in quantum optics. Since this method is independent of protocols and security proofs, it is applicable to Gaussian-modulation and discrete-modulation protocols, to the finite-size regime, and to any proof techniques developed so far and yet to be discovered as well.
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.
Discrete-modulated continuous-variable quantum key distribution protocols are promising candidates for large-scale deployment due to the large technological overlap with deployed modern optical communication devices. The security of discrete modulation schemes has previously been analyzed in the ideal detector scenario in the asymptotic limit. In this work, we calculate asymptotic key rates against collective attacks in the trusted detector noise scenario. Our results show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors.