Optimal propagation distance for maximal biphoton entanglement through the weakly turbulent atmosphere

TL;DR

This paper derives an analytical model for biphoton entanglement propagation through atmospheric turbulence, identifying optimal distances for maximum entanglement, which aids in designing free-space quantum communication systems.

Contribution

It introduces an analytical expression for the biphoton density operator after turbulent propagation, revealing how entanglement persists and identifying optimal propagation distances.

Findings

Entanglement persists despite turbulence-induced purity loss.

Maximum entanglement occurs within a finite propagation distance.

Insights for designing long-distance free-space quantum links.

Abstract

Understanding the influence of atmospheric turbulence on the propagation of entangled biphoton states is essential for free-space quantum communication protocols. Using the extended Huygens-Fresnel principle and the Kolmogorov turbulence model, we derive an analytical expression for the combined density operator of the signal and idler fields generated via SPDC, following propagation through separate turbulent channels. By expressing this density operator in the continuous position basis, we show how the spatial correlations between signal and idler persist through turbulence despite the loss of state purity, as they transition from being quantum to classical in nature. We further identify a finite range of propagation distances over which the angle-OAM entanglement is maximized, which provides valuable insights for designing free-space quantum communication links operating over several kilometers through the turbulent atmosphere.