[Paper Review] Rotation Based Slice Error Correction Protocol for Continuous-variable Quantum Key Distribution and its Implementation with Polar Codes

Xuan Wen, Qiong Li+3 more|arXiv (Cornell University)|Jun 11, 2021

Quantum Information and Cryptography47 references4 citations

TL;DR

This paper proposes a Rotation-based Slice Error Correction (RSEC) protocol for continuous-variable quantum key distribution (CV-QKD), enhancing quantization efficiency by applying random orthogonal rotation to raw data before quantization and deriving a new estimator. The RSEC protocol achieves up to 99% quantization efficiency and maintains ~96% efficiency at low SNRs (0.5, 1), extending the secure distance of CV-QKD to approximately 45 km, with reconciliation efficiency exceeding 95% when implemented with polar codes of 16 Mb block length.

ABSTRACT

Reconciliation is an essential procedure for continuous-variable quantum key distribution (CV-QKD). As the most commonly used reconciliation protocol in short-distance CV-QKD, the slice error correction (SEC) allows a system to distill more than 1 bit from each pulse. However, its quantization efficiency is greatly affected by the noisy channel with a low signal-to-noise ratio (SNR), which usually limits the secure distance to about 30 km. In this paper, an improved SEC protocol, named Rotation-based SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. Experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99\%, and maintains at around 96\% even at the relatively low SNRs $(0.5,1)$, which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with block length of 16 Mb, the RSEC can achieve a reconciliation efficiency of above 95\%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieve a secret key rate of $7.83 imes10^{-3}$ bits/pulse at a distance of 33.93 km (the corresponding SNR value is 1). These results indicate that the proposed protocol significantly improves the performance of SEC and is a competitive reconciliation scheme for the CV-QKD system.

Motivation & Objective

• To address the limited secure distance of conventional slice error correction (SEC) in CV-QKD, which is constrained to ~30 km due to poor performance at low signal-to-noise ratio (SNR).
• To enhance the quantization efficiency of SEC under noisy, low-SNR conditions typical of long-distance quantum channels.
• To develop a reconciliation protocol that maintains high efficiency at low SNR while enabling extraction of more than 1 bit of secret key per pulse.
• To implement the improved protocol using polar codes for practical deployment, ensuring high reconciliation efficiency and finite-size performance.

Proposed method

• Applying a random orthogonal rotation to the raw correlated data from Alice and Bob before quantization to decorrelate noise and reduce information loss.
• Deriving a new slice estimator for quantized sequences based on the rotated data to improve estimation accuracy under low SNR.
• Integrating the RSEC protocol with polar codes for error correction, leveraging their capacity-approaching performance and suitability for finite block lengths.
• Using a block length of 16 Mb for polar codes to evaluate reconciliation efficiency and finite-size performance in practical settings.
• Theoretical analysis of mutual information and Holevo bound to model information-theoretic security limits under various noise conditions.
• Incorporating finite-size effects via an offset factor approximation to evaluate practical secret key rates.

Experimental results

Research questions

• RQ1 Can random orthogonal rotation of raw data improve the quantization efficiency of SEC in low-SNR regimes common in long-distance CV-QKD?
• RQ2 What is the maximum secure distance achievable by an enhanced SEC protocol that maintains high reconciliation efficiency at low SNR?
• RQ3 How does the RSEC protocol compare to conventional SEC in terms of reconciliation efficiency and secret key rate under finite-size and non-ideal physical conditions?
• RQ4 Can polar codes effectively implement the RSEC protocol at scale, achieving high reconciliation efficiency with practical block lengths?
• RQ5 To what extent does the RSEC protocol reduce information loss during quantization compared to standard SEC?

Key findings

• The RSEC protocol achieves a quantization efficiency of up to 99% and maintains approximately 96% efficiency even at low SNRs of 0.5 and 1, significantly outperforming conventional SEC.
• The secure distance of CV-QKD is theoretically extended from ~30 km to approximately 45 km using the RSEC protocol due to improved robustness against channel noise.
• With a polar code block length of 16 Mb, the RSEC protocol achieves a reconciliation efficiency above 95%, surpassing all previous SEC-based schemes.
• At a transmission distance of 33.93 km (SNR = 1), the system achieves a finite-size secret key rate of 7.83 × 10⁻³ bits/pulse, demonstrating practical viability.
• The secret key rate of the RSEC-based system reaches 0.115 of the PLOB bound under non-ideal conditions, compared to only 0.064 for the conventional SEC protocol.
• Theoretical and experimental results confirm that RSEC reduces information loss during quantization and provides a more efficient reconciliation solution for practical CV-QKD systems.