Infinitesimal propagation equation for decoherence of an OAM entangled biphoton in atmospheric turbulence

TL;DR

This paper derives a first order differential equation to model how atmospheric turbulence causes decoherence in orbital angular momentum entangled biphoton states during propagation.

Contribution

It introduces an infinitesimal propagation equation based on the distortion of OAM states in turbulence, providing a new analytical tool for studying decoherence.

Findings

The equation describes entanglement decay in turbulent atmosphere.

Application to a qubit case illustrates the decoherence process.

Provides a foundation for analyzing OAM entanglement in free-space quantum communication.

Abstract

We derive a first order differential equation for the decoherence of an orbital angular momentum entangled biphoton state propagating through a turbulent atmosphere. The derivation is based on the distortion that orbital angular momentum states experience due to propagation through a thin sheet of turbulent atmosphere. This distortion is treated as an infinitesimal transformation leading to a first order differential equation, which we call an infinitesimal propagation equation. The equation is applied to a simple qubit case to show how the entanglement decays.