Generalised Pinching Inequality

Quantum Physics arXiv:2510.19111 (quant-ph) [Submitted on 21 Oct 2025] Title:Generalised Pinching Inequality Authors:Andreas Winter View a PDF of the paper titled Generalised Pinching Inequality, by Andreas Winter View PDF HTML (experimental) Abstract:Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond. Here, we show a very simple proof of it, which lends itself immediately to natural generalisations where the different projections of the measurement have different weights, and where the matrix inequality can be reversed. As an application we show how the generalised pinching inequality in the case of binary measurements gives rise to a novel gentle measurement lemma, where matrix ordering replaces approximation in trace norm. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2510.19111 [quant-ph] (or arXiv:2510.19111v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.19111 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andreas Winter [view email] [v1] Tue, 21 Oct 2025 22:17:29 UTC (8 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalised Pinching Inequality, by Andreas WinterView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: 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?)