Study Defines Optimal Propagation Distance for Maximizing Biphoton Entanglement through Weakly Turbulent Atmosphere

Atmospheric turbulence presents a significant challenge to transmitting quantum information via free-space links, degrading the delicate entanglement necessary for secure communication and distributed sensing. Luchang Niu, Saleem Iqbal, Yang Xu, and Robert W. Boyd from the University of Rochester and University of Ottawa now demonstrate a way to optimise the transmission of entangled photons through such turbulent conditions. The team derives a mathematical description of how entanglement evolves as photons travel through the atmosphere, revealing that spatial correlations between the photons persist even as the overall quantum state loses purity and begins to resemble classical light. Crucially, the research identifies a specific range of distances where angle-orbital angular momentum entanglement is maximised, offering a vital step towards building practical, multi-kilometer free-space quantum communication networks.

Turbulence Degrades Orbital Angular Momentum Entanglement

This research investigates how atmospheric turbulence impacts quantum states of light encoded using orbital angular momentum (OAM), a crucial factor for long-distance free-space quantum communication. Scientists aimed to understand how turbulence degrades entanglement and explore methods to maintain quantum correlations over extended distances. The study employs theoretical modeling, based on the extended Huygens-Fresnel principle and statistical optics, to simulate light propagation through turbulent air. Key findings reveal that turbulence significantly reduces the entanglement of OAM states, posing a major obstacle to practical quantum communication systems.

Larger receiver apertures can help mitigate these effects, and under specific conditions, entanglement can be restored after initial degradation, offering a promising avenue for extending communication range. Orbital angular momentum provides a higher-dimensional alphabet for encoding quantum information compared to traditional polarization-based qubits. Entanglement, a fundamental quantum phenomenon, links particles even over vast distances and is essential for many quantum communication protocols. Atmospheric turbulence, caused by temperature and density variations, randomly distorts light, degrading quantum states.

The extended Huygens-Fresnel principle models wave propagation, accounting for turbulence by treating each point on a wavefront as a source of secondary wavelets. The mutual coherence function mathematically describes the correlation between different points on a wavefront, while receiver aperture averaging reduces turbulence effects by increasing the receiver size. EPR correlations measure entanglement based on the correlations between entangled particles. This research builds upon previous work, including studies demonstrating transverse entanglement migration and the quality of spatial entanglement propagation. Researchers also referenced observations of entanglement revival after turbulence-induced degradation and the use of EPR correlations to quantify high-dimensional entanglement. This work provides a valuable contribution to the field by investigating the effects of atmospheric turbulence on OAM-encoded entanglement, offering insights into the challenges and opportunities for building robust quantum communication systems.

Turbulence Impacts on Entangled Photon Propagation

This study pioneers a method for understanding how atmospheric turbulence affects entangled photons, crucial for free-space quantum communication. Researchers employed the extended Huygens-Fresnel (eHF) principle, a generalization of conventional wave propagation, to model the distortion of light as it travels through turbulent air. This principle accounts for random fluctuations in the atmosphere by treating each point on a wavefront as a source of secondary wavelets, statistically modeling the turbulence’s impact on these wavelets. The eHF principle has proven reliable in previous studies of light propagation through turbulence, providing a robust framework for this investigation.

Scientists mathematically described the propagation of the optical field using an integral equation incorporating the eHF principle, accounting for the distance traveled and the random phase shifts induced by turbulence. To quantify turbulence, the team utilized the Kolmogorov model, a widely accepted statistical description of atmospheric fluctuations, and approximated the turbulence function using a quadratic form. This allowed for an analytical expression of how turbulence affects the light field, defining a coherence length dependent on the refractive index structure constant and the wavelength of light. The study then focused on entangled photon pairs created through spontaneous parametric down-conversion (SPDC).

Researchers modeled the two-photon field using a double Gaussian approximation, describing the spatial correlation between the signal and idler photons at the source. The team then extended the eHF principle to describe the propagation of this two-photon field through turbulence, deriving an equation for the second-order cross-spectral density function. This function characterizes the correlation between the signal and idler photons after they have traveled through the turbulent atmosphere. Crucially, the team assumed that the signal and idler photons experience statistically independent turbulence, simplifying the calculation of the overall phase distortion. By combining this with the second-order cross-spectral density function, scientists obtained a comprehensive description of how turbulence affects the entanglement of the photon pair. The method enables the prediction of how the spatial correlations between entangled photons evolve as they propagate through the atmosphere, providing valuable insights for designing robust free-space quantum communication links over distances of several kilometers.

Turbulence Decoheres Entanglement, Preserves Spatial Correlations

This work details a comprehensive investigation into the propagation of entangled photon pairs through turbulent atmospheric conditions, crucial for advancing free-space quantum communication. Scientists derived an analytical expression describing the combined quantum state of these photons after traveling through separate turbulent channels, allowing for precise modeling of how turbulence affects entanglement. The results demonstrate that while turbulence reduces the purity of the quantum state, spatial correlations between the signal and idler photons persist, transitioning from quantum to classical behaviour as turbulence increases or propagation distance extends. Measurements confirm that the degree of this decoherence, or loss of quantum characteristics, is directly related to both the strength of the turbulence and the distance the photons travel.

The team identified a finite range of propagation distances where angle-orbital angular momentum (OAM) entanglement is maximized, providing valuable insights for designing free-space communication links spanning several kilometers. This optimization is critical for maintaining secure quantum key distribution over practical distances. Further analysis involved quantifying entanglement using the EPR criterion, revealing how the degree of entanglement diminishes with increasing turbulence and propagation distance. The team developed a method for calculating the conditional OAM uncertainty, allowing for precise characterization of entanglement loss.

They also demonstrated that collimating the photon pairs with a thin lens improves the signal quality and reduces the required detector aperture, enhancing the practicality of free-space quantum communication systems. Specifically, the study shows that the joint probability distribution for photon positions can be directly measured using coincidence detection, and the derived equations accurately model this distribution. The team successfully incorporated the effects of turbulence into the equations governing the propagation of Laguerre-Gauss modes, essential for encoding and transmitting quantum information via OAM. These findings provide a robust theoretical framework and practical guidance for overcoming the challenges posed by atmospheric turbulence in free-space quantum communication.

Turbulence Preserves Photon Entanglement Over Distance

This research demonstrates how entangled biphoton states propagate through atmospheric turbulence, a crucial consideration for free-space quantum communication. By applying an extended Huygens-Fresnel principle alongside the Kolmogorov turbulence model, scientists have derived an analytical expression describing the combined density operator of the photon pair, allowing for detailed analysis of entanglement evolution.