Operational Threshold for Spatial Entanglement Survival Under Ionizing Decoherence

Abstract

The resilience of quantum entanglement under irreversible, energy-transferring interactions remains a fundamental question in quantum foundations and emerging quantum technologies. We develop a fully microscopic quantum electrodynamics framework to describe how spatial entanglement evolves when one particle of an entangled pair undergoes dissipative processes such as ionization or inelastic scattering. We show that entanglement decay follows an exponential law governed by recoil-induced momentum diffusion and identify a sharp operational threshold separating quantum-coherent and classical regimes. This threshold depends on whether the cumulative recoil-induced uncertainty exceeds the intrinsic bandwidth of the entangled state. Our results extend decoherence theory beyond Gaussian and weak-coupling models, providing quantitative criteria for entanglement survival in radiative environments and informing the design of robust quantum protocols in quantum sensing, imaging, and radiation-based quantum technologies.