Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties

Quantum Physics arXiv:2608.02745 (quant-ph) [Submitted on 3 Aug 2026] Title:Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties Authors:Fabio Franchini, Salvatore Marco Giampaolo View a PDF of the paper titled Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties, by Fabio Franchini and 1 other authors View PDF HTML (experimental) Abstract:While the full non-stabilizerness (magic) of a quantum state contains local, basis-dependent contributions, a non-local formulation based on a minimization over local unitaries isolates the component associated with genuinely non-local correlations. Within such a framework, the Schmidt-gauge formulation of non-local magic provides a direct connection between genuinely non-local non-stabilizer correlations and the entanglement spectrum of quantum many-body states. Building on the exact Walsh--Hadamard representation introduced in our accompanying Letter, we develop the mathematical theory associated with this formulation. We extend the formalism to arbitrary bipartitions, prove the exactness of the Schmidt gauge for arbitrary $1\times N$ bipartitions, and derive general analytical properties of Schmidt-gauge non-local magic, including entanglement bounds, selection rules, and exact relations with the moments of the normalized Walsh spectrum. This representation also allows to interpret non-local magic as the inverse participation ratio of the Walsh entanglement spectrum, thus relating it to a concentration measure in Walsh space. These results demonstrate that the Walsh--Hadamard representation reveals an underlying discrete harmonic structure that is hidden in the original spectral formulation and provides considerably more than an equivalent expression for Schmidt-gauge non-local magic. Rather, it furnishes the natural mathematical framework for its analytical investigation, placing the theory within the broader context of discrete harmonic analysis. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.02745 [quant-ph] (or arXiv:2608.02745v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.02745 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Salvatore Marco Giampaolo [view email] [v1] Mon, 3 Aug 2026 18:00:12 UTC (16 KB) Full-text links: Access Paper: View a PDF of the paper titled Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties, by Fabio Franchini and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)