# Higher dimensional quantum communication in a curved spacetime: an efficient simulation of the propagation of the wavefront of a photon

## TL;DR

This paper presents an efficient numerical simulation method for the propagation of complex photon wavefronts in inhomogeneous media, with applications to higher-dimensional quantum communication and potential satellite QKD systems.

## Contribution

It introduces a novel simulation approach for complex wavefronts in inhomogeneous media, enabling analysis of high-dimensional quantum communication channels in curved spacetime environments.

## Key findings

- Simulated the propagation of optical vortices in holographic elements.
- Analyzed an OAM volume-holographic sorter.
- Proposed optical analog models for wavefront evolution in Earth's curved spacetime.

## Abstract

A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channel\~Os tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.