Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
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Quantum Physics arXiv:2602.15202 (quant-ph) [Submitted on 16 Feb 2026] Title:Tomography by Design: An Algebraic Approach to Low-Rank Quantum States Authors:Shakir Showkat Sofi, Charlotte Vermeylen, Lieven De Lathauwer View a PDF of the paper titled Tomography by Design: An Algebraic Approach to Low-Rank Quantum States, by Shakir Showkat Sofi and 1 other authors View PDF HTML (experimental) Abstract:We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be obtained solely using standard numerical linear algebra operations. The proposed algebraic matrix completion framework applies to a broad class of generic, low-rank mixed quantum states and, compared with state-of-the-art methods, is computationally efficient while providing deterministic recovery guarantees. Comments: Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Signal Processing (eess.SP); Numerical Analysis (math.NA); Computation (stat.CO) MSC classes: 15A18, 15A69, 15A83, 62H25, 65F30, 65F55, 68Q01, 81P45, Cite as: arXiv:2602.15202 [quant-ph] (or arXiv:2602.15202v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15202 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shakir Showkat Sofi [view email] [v1] Mon, 16 Feb 2026 21:31:47 UTC (102 KB) Full-text links: Access Paper: View a PDF of the paper titled Tomography by Design: An Algebraic Approach to Low-Rank Quantum States, by Shakir Showkat Sofi and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.AI cs.NA eess eess.SP math math.NA stat stat.CO 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)