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Quantum Information Processing

Analysis of information reconciliation algorithms with randomness extractors in quantum key distribution post-processing

Hussan ul Maab, Ijaz Hussain, Zeeshan Alvi

Published Aug 25, 2025• 0 citations
Publisher
DOI
10.1007/s11128-025-04905-4

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In this thesis, we investigate how the combination of quantum physics and information theory could deliver solutions at the forefront of information security, and, in particular, we consider two focus applications: randomness extraction as applied to quantum random number generators and classical processing algorithms for quantum key distribution (QKD). We concentrate on practical applications for such tools. We detail the implementation of a randomness extractor for a commercial quantum random number generator, and we evaluate its performance based on information theory. Then, we focus on QKD as applied to a specific experimental scenario, that is, the one of free-space quantum links. Commercial solutions with quantum links operating over optical fibers, in fact, already exist, but suffer from severe infrastructure complexity and cost overheads. Free-space QKD allows for a higher flexibility, for both terrestrial and satellite links, whilst experiencing higher attenuation and noise at the receiver. In this work, its feasibility is investigated and proven in multiple experiments over links of different length, and in various channel conditions. In particular, after a thorough analysis of information reconciliation protocols, we consider finite-key effects as applied to key distillation, and we propose a novel adaptive real-time selection algorithm which, by leveraging the turbulence of the channel as a resource, extends the feasibility of QKD to new noise thresholds. By using a full-fledged software for classical processing tailored for the considered application scenario, the obtained results are analyzed and validated, showing that quantum information security can be ensured in realistic conditions with free-space quantum links.
Quantum key distribution (QKD), based on quantum mechanics, enables unconditionally secure key exchange even against adversaries with unlimited computing power. As the core of QKD post-processing, information reconciliation (IR) and privacy amplification (PA) ensure key consistency and security by correcting errors and removing leaked information. With the trend toward miniaturized and chip-based QKD systems, post-processing modules require highly integrated designs. FPGAs offer an ideal solution due to their low cost, power efficiency, and flexibility. This paper presents an FPGA-based QKD post-processing architecture using a polar codes-based appending IR algorithm, achieving reconciliation efficiency better than 1.1 under Eµ≥ 0.06 and Rm= 4. A convolution-structured Toeplitz hash module is developed for PA, supporting 53.13 Mbps data rate and 26.45 Mbps key rate with RPA= 0.5. The complete system is implemented on a Xilinx XCKU040 FPGA. Experimental results show support for 176.58 Mbps input, 36.59 Mbps real-time processing, and 17.56 Mbps key output, demonstrating strong performance and engineering suitability. The design features high integration and portability, offering a practical hardware solution for efficient QKD post-processing.