Efficient Reconciliation of Continuous Variable Quantum Key Distribution with Multiplicatively Repeated Non-Binary LDPC Codes

2025-01-19

AI Summary

To address the low efficiency and poor adaptability of classical post-processing in continuous-variable quantum key distribution (CV-QKD) under high-noise, long-distance, and standard-fiber conditions, this paper proposes a single-code reconciliation scheme based on multiplicative-repeat non-binary LDPC codes. We innovatively design a rate-adaptive code construction method that eliminates the need for codebook optimization: a single (2,k)-regular protograph suffices to generate noise-resilient low-density parity-check codes over GF(2) adaptable across the full noise range. Integrated with robust short-block decoding and hardware-friendly architecture, the scheme significantly simplifies encoding and natively supports time-varying channels. Experimentally, it achieves record CV-QKD distances of 192 km over standard single-mode fiber and 240 km over ultra-low-loss fiber—state-of-the-art performance—while maintaining high secret key rates and strong robustness even at short block lengths.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Continuous variable quantum key distribution bears the promise of simple quantum key distribution directly compatible with commercial off the shelf equipment. However, for a long time its performance was hindered by the absence of good classical postprocessing capable of distilling secret-keys in the noisy regime. Advanced coding solutions in the past years have partially addressed this problem enabling record transmission distances of up to 165 km, and 206 km over ultra-low loss fiber. In this paper, we show that a very simple coding solution with a single code is sufficient to extract keys at all noise levels. This solution has performance competitive with prior results for all levels of noise, and we show that non-zero keys can be distilled up to a record distance of 192 km assuming the standard loss of a single-mode optical fiber, and 240 km over ultra-low loss fibers. Low-rate codes are constructed using multiplicatively repeated non-binary low-density parity-check codes over a finite field of characteristic two. This construction only makes use of a (2,k)-regular non-binary low-density parity-check code as mother code, such that code design is in fact not required, thus trivializing the code construction procedure. The construction is also inherently rate-adaptive thereby allowing to easily create codes of any rate. Rate-adaptive codes are of special interest for the efficient reconciliation of errors over time or arbitrary varying channels, as is the case with quantum key distribution. In short, these codes are highly efficient when reconciling errors over a very noisy communication channel, and perform well even for short block-length codes. Finally, the proposed solution is known to be easily amenable to hardware implementations, thus addressing also the requirements for practical reconciliation in continuous variable quantum key distribution.

Problem

• Continuous-Variable Quantum Key Distribution
• High-Noise Environment
• Efficient Key Extraction

Innovation

• Quantum Key Distribution
• Non-binary Coding
• High-noise Resilience