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IEEE International Symposium on Information Theory (ISIT)

Multidimensional reconciliation for continuous-variable quantum key distribution

Anthony Leverrier, Romain Alléaume, Joseph J. Boutros, Gilles Zémor, Philippe Grangier

Published Jul 1, 2008• 29 citations
Publisher

Abstract

We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, relying on the algebraic properties of octonions. By using this coding scheme with an appropriate signal-to-noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended.

DOI
10.1109/isit.2008.4595141

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We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, relying on the algebraic properties of octonions. By using this coding scheme with an appropriate signal-to-noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended.
We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method based on the algebraic properties of octonions. Since the protocol does not use any post-selection, it can be proven secure against arbitrary collective attacks by using well-established theorems on the optimality of Gaussian attacks. By using this coding scheme with an appropriate signal-to-noise ratio, the distance for a secure continuous-variable quantum key distribution can be significantly extended.
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.
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 quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.
We propose an efficient logical layer-based reconciliation method for continuous-variable quantum key distribution (CVQKD) to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the low-dimensional (scalar) space, and the reconciliation can be extended to arbitrary dimensions. The CVQKD systems allow an unconditionally secret communication over standard telecommunication networks. To exploit the real potential of CVQKD a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of the CVQKD protocols. The reconciliation is a post-processing step separated from the transmission of quantum states, which is aimed to derive the secret key from the raw data. The reconciliation process of correlated Gaussian variables is a complex problem that requires either tomography in the physical layer that is intractable in a practical scenario, or high-cost calculations in the multidimensional spherical space with strict dimensional limitations. To avoid these issues, we define the low-dimensional reconciliation. We prove that the error probability of one-dimensional reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow for significantly improving the currently available key rates and transmission distances of CVQKD.