Double Markovity for quantum systems

Quantum Physics arXiv:2601.09995 (quant-ph) [Submitted on 15 Jan 2026] Title:Double Markovity for quantum systems Authors:Masahito Hayashi, Jinpei Zhao View a PDF of the paper titled Double Markovity for quantum systems, by Masahito Hayashi and Jinpei Zhao View PDF Abstract:The subadditivity-doubling-rotation (SDR) technique is a powerful route to Gaussian optimality in classical information theory and relies on strict subadditivity and its equality-case analysis, where double Markovity is a standard tool. We establish quantum analogues of double Markovity. For tripartite states, we characterize the simultaneous Markov conditions A-B-C and A-C-B via compatible projective measurements on B and C that induce a common classical label J yielding A-J-(BC). For strictly positive four-party states, we show that A-(BD)-C and A-(CD)-B hold if and only if A-D-(BC) holds. These results remove a key bottleneck in extending SDR-type arguments to quantum systems. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.09995 [quant-ph] (or arXiv:2601.09995v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.09995 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Masahito Hayashi [view email] [v1] Thu, 15 Jan 2026 02:15:49 UTC (89 KB) Full-text links: Access Paper: View a PDF of the paper titled Double Markovity for quantum systems, by Masahito Hayashi and Jinpei ZhaoView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)