Security of deterministic key distribution with higher-dimensional systems

TL;DR

This paper investigates the security of two-way quantum key distribution protocols in higher-dimensional systems, demonstrating increased robustness and a dimensional advantage against eavesdropping attacks.

Contribution

It extends security analysis to arbitrary finite dimensions, showing improved security and key rates without relying on entangled states.

Findings

Higher-dimensional systems offer increased security against eavesdropping.

Secret keys can be generated at greater interception strengths in higher dimensions.

The protocol's robustness improves as the system dimension increases.

Abstract

We analyze the security of two-way quantum key distribution using arbitrary finite-dimensional systems, considering both individual and collective eavesdropping attacks, without the effective use of entangled states, by incorporating two mutually unbiased bases and Heisenberg-Weyl operators in higher dimensions. For individual attacks, we consider cloning operations by the eavesdropper and demonstrate a dimensional advantage where secret keys can be generated for greater strengths of interception. To analyze security under collective attacks, we employ a purification scheme and derive the key rate using entropic uncertainty relations. Further, we exhibit how the protocol is more robust against eavesdropping with increasing dimension of the systems used, and compare the performance with that of the entangled two-way secure dense coding protocol when the presence of the eavesdropper is modeled by correlated and uncorrelated noise.