An Improved Correction Term for Dimension Reduction in Quantum Key Distribution

TL;DR

This paper introduces a tighter correction term for dimension reduction in quantum key distribution, improving the accuracy of security proofs and reducing computational complexity by better handling measurement operators.

Contribution

A novel correction term that interpolates between extreme cases, enhancing the precision and efficiency of dimension reduction in QKD security analysis.

Findings

Provides a tighter correction term for nearly block-diagonal measurements

Reduces the required dimension of the subspace for security proofs

Improves computational efficiency in QKD dimension reduction

Abstract

The dimension reduction method enables security proofs of quantum key distribution (QKD) protocols that are originally formulated in infinite dimensions via reduction to a tractable finite-dimensional optimization. The reduction of dimensions is associated with a correction term in the secret key rate calculation. The previously derived correction term is loose when the protocol measurements are nearly block-diagonal with respect to the projection onto the reduced finite-dimensional subspace. Here, we provide a tighter correction term. It interpolates between the two extreme cases where all measurement operators are block-diagonal, and where at least one has maximally large off-diagonal blocks. This new correction term can reduce the computational overhead of applying the dimension reduction method by reducing the required dimension of the chosen subspace.