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arXiv:2602.05526

Arithmetic Reconciliation for CVQKD: Challenges and Feasibility

Rávilla R. S. Leite, Juliana M. de Assis, Micael A. Dias, Francisco M. de Assis

quant-phSubmitted Feb 5, 2026• Announced Feb 6, 2026• 0 citations
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Abstract

Continuous variable quantum key distribution allows two legitimate parties to share a common secret key and encompasses reconciliation protocols. A relatively new reconciliation protocol, Arithmetic Reconciliation, presents low complexity and has increasing reconciliation efficiency with lower SNRs. In this paper, we obtain reconciliation efficiencies for this protocol in realistic scenarios, by means of estimation of mutual information, and we also present rates for sequence match of secret keys by Alice and Bob. Results show that this technique is feasible and promising to continuous variable quantum key distribution applications.

Comments
9 pages, 10 pages. Journal paper, under review for submission

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•Aug 6, 2013•11 citations
Continuous variable quantum key distribution allows two legitimate parties to share a common secret key and encompasses reconciliation protocols. A relatively new reconciliation protocol, Arithmetic Reconciliation, presents low complexity and has increasing reconciliation efficiency with lower SNRs. In this paper, we obtain reconciliation efficiencies for this protocol in realistic scenarios, by means of estimation of mutual information, and we also present rates for sequence match of secret keys by Alice and Bob. Results show that this technique is feasible and promising to continuous variable quantum key distribution applications.
The performance of a continuous-variable quantum key distribution (CVQKD) protocol depends on the efficiency of the post-processing of measurement results. The post-processing methods extract statistical information from the raw data, establish the mutual knowledge between the parties, and produce a final key that provides absolute security. The post-processing phase is a bottleneck in CVQKD with crucial importance to the efficiency and protocol attributes. Post-processing uses the raw data of the parties generated by the quantum-level transmission and a classical authenticated channel to generate a secret key between the parties. The current reconciliation procedures require high-complexity coding with moderate resulting efficiency. Here we define an optimization method for post-processing in continuous-variable quantum key distribution. The reconciliation method achieves additive Gaussian noise on the random secret for arbitrarily low dimensional blocks. The model consumes all information from the raw data blocks to provide maximal efficiency and security via standard operations. The results can be realized by generic Gaussian coding schemes, allowing an easily implementation for experimental CVQKD protocols.
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.
Information reconciliation is a crucial process in continuous-variable quantum key distribution(CV-QKD) systems. The slice error correction (SEC) reconciliation is appropriate for short-distance CV-QKD. However, the efficiency of SEC reconciliation schemes is significantly influenced by noisy channels with low signal-to-noise ratios (SNRs). In this paper, we present an enhanced information reconciliation scheme, termed AC-SEC reconciliation, which adds the new Gaussian sequences c with the original Gaussian sequences y before quantization in the SEC reconciliation to obtain secret key sequences with high variance and reduce noise interferences. Simulation results demonstrate that compared with the traditional SEC reconciliation, the proposed information reconciliation has lower frame error rate (FER) and higher reconciliation efficiency, which can increase the secret key rate (SKR).
The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses ddd-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's ttt-distribution. Therefore, we propose a ttt-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed ttt-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.
We introduce a new and applicable technique for reconciling continuous-variable quantum key distribution (CVQKD) based on Gaussian modulation of coherent states. Its key feature is the application of the cumulative distribution function (CDF) to map Gaussian variables onto uniform [0,1][{0,1}][0,1] random variables, which are then expanded into Bernoulli (1/2)(1/2)(1/2) random variables, following the principles of Arithmetic Coding. This approach replaces the complex quantization procedures inherent in Slice Reconciliation, while also normalizing the variables of interest to generate the secret key, and thus avoiding the complexities associated with Multidimensional Reconciliation algorithms. The protocol does not use any post-selection, thus it can be proved secure against arbitrary collective attacks.
The two-way continuous-variable quantum key distribution (CVQKD) systems allow higher key rates and improved transmission distances over standard telecommunication networks in comparison to the one-way CVQKD protocols. To exploit the real potential of two-way CVQKD systems a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of a two-way CVQKD system. 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 propose an efficient logical layer-based reconciliation method for two-way 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 scalar space and the reconciliation can be extended to arbitrary high dimensions. We prove that the error probability of scalar reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow to significantly improve the currently available key rates and transmission distances of two-way CVQKD. The proposed scalar reconciliation can also be applied in one-way systems as well, to replace the existing reconciliation schemes.