Quantum Measurement as a Metric-Degeneracy Process

We formulate quantum measurement as a continuous degeneration of the correlationmetric induced by the quantum Fisher information. Instead of postulatinginstantaneous state projection, measurement is described as an environment-driventrajectory along which the Fisher metric associated with correlation-generatingobservables progressively loses rank. We show that the induced correlation metric collapses nonlinearly as g_corr ~ Lambda_eff^2 * (1 - s), where Lambda_eff is a calibrated interaction strength and s is a state-dependentcorrelation amplitude factor. Numerical simulations reveal a residual Fisher floor under damping channels whosebasis does not commute with the measurement basis. In the dephasing-calibratedscheme used here, non-commuting amplitude damping induces a nonzero interceptb(gamma) defined by the near-Lambda_eff -> 0 limit. The leading dependence of thisintercept is linear in gamma for correlated generators, including the exactrelation b_rel(gamma) = 2 * gamma for the isotropic Heisenberg interaction. Projective measurement emerges as the singular limit of dynamical metricdegeneracy.