Equiangular quantum key distribution in more than two dimensions

TL;DR

This paper extends quantum key distribution protocols to higher-dimensional qudits using equiangular frames, enhancing security and robustness against eavesdropping compared to qubit-based systems.

Contribution

It introduces methods for constructing equiangular frames in arbitrary dimensions and applies them to develop more secure qudit-based key distribution protocols.

Findings

Protocols for 4 and 16-dimensional qudits are constructed.

The use of equiangular frames increases robustness against eavesdropping.

Security analysis shows advantages over qubit-based protocols.

Abstract

We extend the spherical code based key distribution protocols to qudits with dimensions 4 and 16 by constructing equiangular frames and their companions. We provide methods for equiangular frames in arbitrary dimensions for Alice to use and the companion frames, that has one antipode to eliminate one of the possibilities, made up of qudits with $N=4,16$ as part of Bob's code. Non-orthogonal bases that form positive operator valued measures can be constructed using the tools of frames (overcomplete bases of a Hilbert space) and here we apply them to key distribution that are robust due to large size of the bases making it hard for eavesdropping. We demonstrate a method to construct a companion frame for an equiangular tight frame for $\complexes^{p-1}$ generated from the discrete Fourier transform, where $p$ is any odd prime. The security analysis is based on the assumption restricting possible attacks to intercept/resend scenario highlighting the advantages of a qudit over qubit-based protocols.