Global Non-Identifiability of Fubini-Study Geometry from Complete One-Period Endpoint Data

Quantum Physics arXiv:2608.10051 (quant-ph) [Submitted on 10 Aug 2026] Title:Global Non-Identifiability of Fubini-Study Geometry from Complete One-Period Endpoint Data Authors:Rashid Ahmad View a PDF of the paper titled Global Non-Identifiability of Fubini-Study Geometry from Complete One-Period Endpoint Data, by Rashid Ahmad View PDF HTML (experimental) Abstract:We establish a global, worst-case non-identifiability theorem for periodically driven finite-dimensional quantum systems. On the unrestricted smooth periodic Hamiltonian class, we show that the period-averaged Fubini-Study metric component of a fixed initial state cannot, in general, be reconstructed from exact one-period propagators indexed by every starting time and external parameter. Thus, even complete starting-time-resolved endpoint data are insufficient to determine this intra-period geometric quantity. The obstruction is characterized exactly. The starting-time-indexed endpoint data determine the conjugation path of the monodromy, but not its particular unitary lift. On each fixed-monodromy slice, the observational fibres are precisely the right orbits generated by smooth parameter-dependent based loops taking values in the pointwise centralizer of the monodromy. The Fubini-Study functional is not invariant under this fibre action and therefore does not factor through the endpoint observation map. An explicit real-analytic two-level witness demonstrates the obstruction within a commuting, one-generator Hamiltonian family, so neither non-Abelian time ordering nor Floquet-logarithm ambiguity is required. A continuous family of Hamiltonians produces identical starting-time-indexed one-period endpoint data while yielding different, and on the unrestricted class arbitrarily separated, period-averaged Fubini-Study geometry. Non-identifiability persists under any prescribed uniform bound on the parameter derivative of the Hamiltonian. The result is a deterministic global statement, not a claim of generic non-identifiability or experimental impossibility. It identifies a precise information gap between complete one-period endpoint data and full intra-period dynamics: the missing information is the unitary lift of the observed monodromy path rather than ordinary scalar phase freedom. Comments: Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph) Cite as: arXiv:2608.10051 [quant-ph] (or arXiv:2608.10051v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.10051 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rashid Ahmad [view email] [v1] Mon, 10 Aug 2026 15:33:19 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Global Non-Identifiability of Fubini-Study Geometry from Complete One-Period Endpoint Data, by Rashid AhmadView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.other math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)