A practical framework for analyzing high-dimensional QKD setups

TL;DR

This paper introduces an efficient analytical framework using semi-definite programming duals and entanglement-witness inspired operators to compute key rates in high-dimensional quantum key distribution systems, overcoming computational limitations.

Contribution

It presents a novel, flexible method combining semi-definite program duals and matrix completion techniques for efficient key rate calculation in high-dimensional QKD setups.

Findings

Enables efficient key rate computation for large encoding dimensions.

Incorporates matrix completion to improve bounds on key rates.

Applicable to time- and frequency-bin entangled photon systems.

Abstract

High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints; thus, accessible dimensions are far exceeded by progress in HD photonics, bringing forth a need for efficient methods to compute key rates for large encoding dimensions. In response to this problem, we present a flexible analytic framework facilitated by the dual of a semi-definite program and diagonalizing operators inspired by entanglement-witness theory, enabling the efficient computation of key rates in high-dimensional systems. To facilitate the latter, we show how matrix completion techniques can be incorporated to effectively yield improved, computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond.