Structure and Classification of Matrix Product Quantum Channels
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Quantum Physics arXiv:2603.19866 (quant-ph) [Submitted on 20 Mar 2026] Title:Structure and Classification of Matrix Product Quantum Channels Authors:Giorgio Stucchi, J. Ignacio Cirac, Rahul Trivedi, Georgios Styliaris View a PDF of the paper titled Structure and Classification of Matrix Product Quantum Channels, by Giorgio Stucchi and 3 other authors View PDF Abstract:We develop a framework for Matrix Product Quantum Channels (MPQCs), a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated tensor, that admit a local purification. We show that their purifying isometry can always be implemented by a constant-depth brickwork quantum circuit, implying that such channels generate only short-range correlations. In contrast to the unitary setting, where one-dimensional quantum cellular automata (in one-to-one correspondence with matrix product unitaries) carry a nontrivial index, we prove that all locally purified channels belong to a single phase, that is, they can be continuously deformed into one another. We then extend the framework to a broader class of translation-invariant channels capable of generating long-range entanglement and show that these remain deterministically implementable in constant depth using two rounds of measurements and feedforward. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph) Cite as: arXiv:2603.19866 [quant-ph] (or arXiv:2603.19866v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.19866 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Giorgio Stucchi [view email] [v1] Fri, 20 Mar 2026 11:34:36 UTC (242 KB) Full-text links: Access Paper: View a PDF of the paper titled Structure and Classification of Matrix Product Quantum Channels, by Giorgio Stucchi and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.str-el 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?) 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?)