Quantum Fisher Information Connection to Quantum Gravitational Coupling: Semiclassical Justification

This paper rigorously establishes a theoretical justification connecting Quantum Fisher Information (QFI) directly to gravitational coupling strength within a semiclassical quantum gravity context. Starting from fundamental quantum estimation theory and semiclassical Einstein equations, we demonstrate how gravitational interaction strength emerges naturally as a consequence of quantum measurement uncertainty, as quantified by QFI. This result provides a robust quantum informational foundation for gravitational coupling suppression at high energies.