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International Conference on Transparent Optical Networks

Impact of Limited Classical Channel Bandwidth on the Secret Key Rate of a CV-QKD System

Nuno A. Silva, Margarida Almeida, Nelson Jesus Muga, Armando N. Pinto

Published Jul 14, 2024• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) can extract secret keys in an efficient and practical manner using off-the-shelf telecommunication equipment. This sets CV-QKD as a key technology for implementation in optical fiber networks already deployed in the field. Notwithstanding, the extraction of secret keys in CV-QKD requires the exchange of information, not only on a quantum channel, but also on an authenticated and public classical channel. The classical channel is required to exchange part of the coherent states to aid with the parameter estimation step to conclude on the secrecy of the extracted key, and to exchange side information essential to the reconciliation step. Here, we study the bandwidth demand of the information exchanged in the classical channel and how it can impact the extraction key rate of a CV-QKD system. The post-processing step consuming the highest bandwidth of the classical channel is the reconciliation step, due to the exchange of the side information. We consider different dimensions for the multidimensional reconciliation demanding different bandwidths on the classical channel and compute the allowed extraction key rate depending on the performance of the method, in terms of frame error rate.

DOI
10.1109/icton62926.2024.10648210

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Continuous-variable quantum key distribution (CV-QKD) can extract secret keys in an efficient and practical manner using off-the-shelf telecommunication equipment. This sets CV-QKD as a key technology for implementation in optical fiber networks already deployed in the field. Notwithstanding, the extraction of secret keys in CV-QKD requires the exchange of information, not only on a quantum channel, but also on an authenticated and public classical channel. The classical channel is required to exchange part of the coherent states to aid with the parameter estimation step to conclude on the secrecy of the extracted key, and to exchange side information essential to the reconciliation step. Here, we study the bandwidth demand of the information exchanged in the classical channel and how it can impact the extraction key rate of a CV-QKD system. The post-processing step consuming the highest bandwidth of the classical channel is the reconciliation step, due to the exchange of the side information. We consider different dimensions for the multidimensional reconciliation demanding different bandwidths on the classical channel and compute the allowed extraction key rate depending on the performance of the method, in terms of frame error rate.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use ofddd-dimensional reconciliation withd>8d > 8d>8to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.
Continuous variable quantum key distribution (CV-QKD) allows the distribution of symmetric keys in a secure manner. CV-QKD systems can extract keys at its maximum rate when using Gaussian modulation (GM). Nonetheless, GM demands high-capacity random number sources and tends to be very hard to approach in practice. To circumvent these disadvantages, higher-order probabilistic -shaped discrete modulation (DM) can be used. State-of-the-art works compute the key rates of DM-CV-QKD systems considering a fixed value for the reconciliation efficiency and do not take into account the frame error rate (FER) of the system, thus over or under estimating the key rates. In this work, we study the security bounds of CV-QKD systems considering probabilistic shaped DM formats with 256-symbols in the finite-size regime. This accounting for the true value of the reconciliation efficiency, and the FER of the information reconciliation step. Both conventional and hexagonal 256-quadrature amplitude modulation (QAM) constellations yield higher key rates than 256-amplitude and phase shift keying (APSK) constellations, with 256-QAM constellations being indistinguishable in performance with GM for high transmission distances. Minimum signal-to-noise ratio (SNR) values were fixed from a FER analysis through a CV-QKD simulation allowing for key extraction considering different FER levels. Lower FER values are associated with higher SNRs in the system and thus lower achievable transmission distances. Nonetheless, the FER maximizing the extraction key rate is not null. Our results show that the extraction key rate is maximized by SNR adjustment which should have in account both the reconciliation efficiency and the FER.
Quantum Key Distribution (QKD) is, nowadays, the dominant practical application in the quantum technologies field. Nevertheless, extracting secure keys from a physical implementation of a QKD system remains a complicated procedure. In this paper, post-processing algorithms were implemented to extract secret keys from a Continuous-Variable QKD (CV-QKD) system. The Discrete Modulated Four State CV-QKD protocol was considered due to lower complexity in the reconciliation procedure. The secret keys were extracted considering Maximum-Likelihood Estimators (MLEs) for parameter estimation, Iterative Low-Density Parity Check (LDPC) codes complemented with the Sum-Product Algorithm and error groups iterative reconciliation for information reconciliation, and the Toeplitz matrix as the universal hash function for privacy amplification. The post-processing algorithms were applied to extract secret keys from a simulated implementation of the Discrete Modulated Four State CV-QKD protocol, with double homodyne detection.
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.
Abstract The reconciliation method for continuous variable quantum key distribution systems is usually chosen based on its reconciliation efficiency. Nonetheless, one must also consider the requirements of each reconciliation method in terms of the amount of information transmitted on the classical channel. Such may limit the achievable key rates. For instance, multidimensional reconciliation of dimension 8 demands a classical channel bandwidth 43 times greater than that of the quantum channel baud rate. Decreasing the dimension to 4 halves the required bandwidth, allowing for higher quantum channel baud rates and higher key rates for shorter transmission distances, despite the lesser reconciliation performance.