Gluing Randomness via Entanglement: Tight Bound from Second R\'enyi Entropy
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Quantum Physics arXiv:2601.16454 (quant-ph) [Submitted on 23 Jan 2026] Title:Gluing Randomness via Entanglement: Tight Bound from Second Rényi Entropy Authors:Wonjun Lee, Hyukjoon Kwon, Gil Young Cho View a PDF of the paper titled Gluing Randomness via Entanglement: Tight Bound from Second R\'enyi Entropy, by Wonjun Lee and 2 other authors View PDF HTML (experimental) Abstract:The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local random unitaries to generate global random states by effectively gluing randomness across the system. Specifically, we demonstrate that approximate random states can be produced from an entangled state $|\psi\rangle$ through the application of local random unitaries. We show that the resulting ensemble forms an approximate state design with an error saturating as $\Theta(e^{-\mathcal{N}_2(\psi)})$, where $\mathcal{N}_2(\psi)$ is the second Rényi entanglement entropy of $|\psi\rangle$. Furthermore, we prove that this tight bound also applies to the second Rényi entropy of coherence when the ensemble is constructed using coherence-free operations. These results imply that, when restricted to resource-free gates, the quality of the generated random states is determined entirely by the resource content of the initial state. Notably, we find that among all $\alpha$-Rényi entropeis, the second Rényi entropy yields the tightest bounds. Consequently, these second Rényi entropies can be interpreted as the maximal capacities for generating randomness using resource-free operations. Finally, moving beyond approximate state designs, we utilize this entanglement-assisted gluing mechanism to present a novel method for generating pseudorandom states in multipartite systems from a locally entangled state via pseudorandom unitaries in each of parties. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2601.16454 [quant-ph] (or arXiv:2601.16454v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.16454 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Wonjun Lee [view email] [v1] Fri, 23 Jan 2026 05:17:44 UTC (271 KB) Full-text links: Access Paper: View a PDF of the paper titled Gluing Randomness via Entanglement: Tight Bound from Second R\'enyi Entropy, by Wonjun Lee and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el 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?)