The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric

Quantum Physics arXiv:2608.21437 (quant-ph) [Submitted on 17 Aug 2026] Title:The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric Authors:E. A. Ramirez Trino, M. A. Rajabpour View a PDF of the paper titled The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric, by E. A. Ramirez Trino and M. A. Rajabpour View PDF HTML (experimental) Abstract:Stabilizer Rényi entropies compress the distribution of squared Pauli expectation values of a pure quantum state into scalar measures of nonstabilizerness. Here we show that, before this compression, the distribution has a remarkably simple information-geometric structure. For any smooth pure-state family of $N$ qubits, its classical Fisher information matrix is exactly twice the quantum Fisher information matrix of the state at every regular point. This information can be accessed directly: by preparing the state together with its complex conjugate and performing pairwise Bell measurements between corresponding qubits, one samples the same Pauli distribution and saturates the quantum Fisher information matrix of the conjugate pair. The readout is fixed and does not depend on the number of estimated parameters or on the particular pure-state sensing model. We show that the origin of this result is more general than Pauli algebra: conjugation identifies the doubled pure state with the vectorized density operator, whose coordinates are real in any Hermitian Hilbert--Schmidt operator basis. The situation changes for mixed states, for which the Bell probabilities no longer coincide with normalized squared Pauli expectation values and the same fixed readout is generally not optimal. We derive an exact positive-semidefinite expression for the missing Fisher information, identifying the components of the state variation that are invisible to Bell sampling. Our results reveal a direct connection between stabilizer Rényi statistics, quantum-state geometry, and fixed multiparameter readout. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph) Cite as: arXiv:2608.21437 [quant-ph] (or arXiv:2608.21437v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.21437 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Eddy Ariel Ramirez Trino [view email] [v1] Mon, 17 Aug 2026 23:23:59 UTC (278 KB) Full-text links: Access Paper: View a PDF of the paper titled The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric, by E. A. Ramirez Trino and M. A. RajabpourView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.stat-mech 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?)