A Bundle Isomorphism Relating Complex Velocity to Quantum Fisher Operators

Quantum Physics [Submitted on 14 Apr 2026] A Bundle Isomorphism Relating Complex Velocity to Quantum Fisher Operators Jorge Meza-Domínguez We show that averaging matter dynamics over stochastic gravitational fluctuations gives rise to a complex velocity field \(\eta_{\mu} = \pi_{\mu} - i u_{\mu}\) living as a section of the pullback bundle \(E = \pi_{2}^{*}(T^{*}M)\to \mathcal{C}\times M\). We prove that \(\eta_{\mu}\) is isomorphic, via the Schrödinger representation, to the symmetric logarithmic derivative (SLD) operator \(L_{\mu}\) on the Hilbert space \(\mathcal{H}_{x} = L^{2}(\mathcal{C})\), up to a trace-zero projection. This isomorphism \(\widetilde{\mathcal{T}}:\Gamma (E / \sim)\to \Gamma (\mathcal{L})\) is a bundle isomorphism preserving the flat \(U(1)\) connection (proved in \cite{meza2026topological}) and the quantum Fisher metric. The quantum Fisher information metric \(g_{\mu \nu}^{\mathrm{FS}}\) is expressed directly in terms of \(\eta_{\mu}\) as \(g_{\mu \nu}^{\mathrm{FS}} = - \frac{4m^{2}}{\hbar^{2}}\mathrm{Re}\langle (\eta_{\mu} - \langle \eta_{\mu}\rangle)(\eta_{\nu} - \langle \eta_{\nu}\rangle)\rangle_{\mathcal{P}}\). The holonomy of \(\eta_{\mu}\) is quantized, leading to topological phases observable in atom interferometry. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Quantum Algebra (math.QA) Cite as: arXiv:2604.12187 [quant-ph]   (or arXiv:2604.12187v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.12187 Focus to learn more Submission history From: Jorge Dettle Meza Domínguez [view email] [v1] Tue, 14 Apr 2026 01:35:43 UTC (8 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.IT gr-qc math math-ph math.IT math.MP math.QA References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)