How gravitational fluctuations degrade the high-dimensional spatial entanglement

TL;DR

This paper investigates how gravitational fluctuations in curved spacetime affect the coherence and entanglement of high-dimensional orbital angular momentum (OAM) photons, revealing increased vulnerability of entanglement in such conditions.

Contribution

The study provides an analytical framework for understanding the impact of spacetime fluctuations on OAM photon entanglement and demonstrates the degradation of entanglement in curved spacetime environments.

Findings

Higher-dimensional OAM entanglement is more susceptible to spacetime fluctuations.

Gravitational fluctuations cause OAM not to remain conserved during propagation.

Entanglement degradation is characterized by purity and negativity metrics.

Abstract

Twisted photons carrying orbital angular momentum (OAM) are competent candidates for future interstellar communications. However, the gravitational fluctuations are ubiquitous in spacetime. Thus a fundamental question arises naturally as to how the gravitational fluctuations affect the coherence and the degree of high-dimensional OAM entanglement when twisted photons travel across the textures of curved spacetime. Here, we consider the covariant scalar Helmholtz equations and the Minkowski metric with fluctuations of Gaussian distribution and formulate analytically the equations describing the motion for twisted light in the Laguerre-Gaussian mode space. It is seen that the OAM cannot remain conserved in the presence of gravitational fluctuations. Furthermore, two-photon density matrices are derived for interstellar OAM quantum entanglement distribution, and the degree of entanglement degradation is characterized by purity and negativity. It is revealed that the higher-dimensional OAM entanglement is more susceptible to spacetime fluctuations. We believe that our findings will be of fundamental importance for the future interstellar quantum communications with twisted photons.