We establish a rigorous bundle isomorphism between the complex velocity field \(η_μ = π_μ - i u_μ\), obtained by averaging matter dynamics over stochastic gravitational fluctuations, and the symmetric logarithmic derivative (SLD) operator \(L_μ\) of quantum estimation theory. The isomorphism \(\widetilde{\mathcal{T}}: Γ(E/{\sim}) \to Γ(\mathcal{L})\) maps gauge-equivalence classes of sections of the pullback bundle \(E = π_2^*(T^*M)\) over \(\mathcal{C} \times M\) to SLD operators on the Hilbert space \(\mathcal{H}_0 = L^2(\mathcal{C}, ν_0)\), where \(\mathcal{C}\) is the infinite-dimensional Fréchet manifold of matter fields and \(ν_0\) is a fixed Gaussian measure. We prove that \(\widetilde{\mathcal{T}}\) and the associated quantum Fisher metric are independent of the choice of \(ν_0\), rendering the construction intrinsic to the physical probability density. The Fisher metric acquires a simple form in terms of \(η_μ\): \(g_{μν}^{\mathrm{FS}} = -\frac{4m^2}{\hbar^2} \operatorname{Re}\langle(η_μ - \langleη_μ\rangle) (η_ν - \langleη_ν\rangle)\rangle_{\mathcal{P}}\). As a consequence, the flat \(U(1)\) connection defined by \(η_μ\) yields a quantized holonomy for non-contractible spacetime loops, predicting topological phases observable in atom interferometry.

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