Rethinking quantum smooth entropies: Tight one-shot analysis of quantum privacy amplification
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Quantum Physics arXiv:2603.04493 (quant-ph) [Submitted on 4 Mar 2026] Title:Rethinking quantum smooth entropies: Tight one-shot analysis of quantum privacy amplification Authors:Bartosz Regula, Marco Tomamichel View a PDF of the paper titled Rethinking quantum smooth entropies: Tight one-shot analysis of quantum privacy amplification, by Bartosz Regula and Marco Tomamichel View PDF HTML (experimental) Abstract:We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic constraints. Our main tool is a new class of smooth conditional entropies defined by lifting classical smooth divergences through measurements. For the key case of measured smooth Rényi divergence of order 2, we show that this can be alternatively understood as allowing for smoothing over not only states, but also non-positive Hermitian operators. Building on this, we establish a tightened leftover hash lemma, significantly improving over all known smooth min-entropy bounds on quantum privacy amplification and recovering the sharpest classical achievability results. We extend these methods to decoupling, the coherent analogue of randomness extraction, obtaining a corresponding improved one-shot bound. Relaxing our smooth entropy bounds leads to one-shot achievability results in terms of measured Rényi divergences, which in the asymptotic i.i.d. limit recover the state-of-the-art error exponent of [Dupuis, arXiv:2105.05342]. We show an approximate optimality of our results by giving a matching one-shot converse bound up to additive logarithmic terms. This yields an optimal second-order asymptotic expansion of privacy amplification under trace distance, establishing a significantly tighter one-shot achievability result than previously shown in [Shen et al., arXiv:2202.11590] and proving its optimality for all hash functions. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph) Cite as: arXiv:2603.04493 [quant-ph] (or arXiv:2603.04493v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.04493 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Bartosz Regula [view email] [v1] Wed, 4 Mar 2026 19:00:01 UTC (59 KB) Full-text links: Access Paper: View a PDF of the paper titled Rethinking quantum smooth entropies: Tight one-shot analysis of quantum privacy amplification, by Bartosz Regula and Marco TomamichelView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.IT math math-ph math.IT 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?)