Arbitrarily-high-dimensional reconciliation via cross-rotation for continuous-variable quantum key distribution

TL;DR

This paper introduces a cross-rotation scheme that enables high-dimensional information reconciliation in continuous-variable quantum key distribution, significantly improving efficiency and extending transmission distances.

Contribution

It proposes a novel cross-rotation method for arbitrarily high-dimensional reconciliation, overcoming previous limitations and reducing communication overhead.

Findings

64-dimensional cross-rotation nearly reaches the theoretical upper bound

The method significantly improves reconciliation efficiency in high dimensions

Simulation confirms practical viability of the approach

Abstract

Multidimensional rotation serves as a powerful tool for enhancing information reconciliation and extending the transmission distance in continuous-variable quantum key distribution (CV-QKD). However, the lack of closed-form orthogonal transformations for high-dimensional rotations has limited the maximum reconciliation efficiency to channels with 8 dimensions over the past decade. This paper presents a cross-rotation scheme to overcome this limitation and enable reconciliation in arbitrarily high dimensions, constrained to even multiples of 8. The key treatment involves reshaping the string vector into matrix form and applying orthogonal transformations to its columns and rows in a cross manner, thereby increasing the reconciliation dimension by one order per cross-rotation while significantly reducing the communication overhead over the classical channel. A rigorous performance analysis is also presented from the perspective of achievable sum-rate. Simulation results demonstrate that 64-dimensional cross-rotation nearly approaches the upper bound, making it a recommended choice for practical implementations.