Operational Threshold for Spatial Entanglement Survival Under Ionizing Decoherence

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 recoilinduced uncertainty exceeds the intrinsic bandwidth of the entangled state. Our results provide a quantitative, first-principles criterion for entanglement survival under a specific class of radiative interactions, complementing Gaussian and weak-coupling models. This framework offers a foundational step towards designing robust quantum protocols in sensing, imaging, and radiation-based technologies where energy transfer is significant.