Experimental Design for Measuring the Inverse-Roughness Constant of Quantum Coherence

A companion paper [1] derived an inverse-roughness law for quantum coherence length: L_c = K_lab / R_n, where L_c is the entanglement coherence length, R_n is the refractive-index gradient roughness of the intervening medium, and K_lab is a proportionality constant. The hyperbolic form of this relationship was derived from geometric principles within the Field Intrinsic Gravity Induced Density (FIGID) framework, but the constant K_lab has not been measured. This paper presents an experimental protocol for determining K_lab in optical fiber by systematically varying the refractive-index roughness through controlled thermal perturbation and measuring the resulting entanglement fidelity as a function of fiber length. The protocol uses standard entangled photon sources, commercially available fiber, and established coincidence-counting techniques. If L_c × R_n = constant across multiple roughness settings within a single medium, the hyperbolic form is confirmed and K_lab is determined. The protocol is designed to be executable by any quantum optics laboratory with an entanglement distribution setup.