Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains

[2509.10700] Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2509.10700 (quant-ph) [Submitted on 12 Sep 2025 ( v1 ), last revised 28 Aug 2026 (this version, v4)] Title: Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains Authors: E. A. Ramirez Trino , M. A. Rajabpour View PDF HTML (experimental) Abstract: Shannon-Rényi and stabilizer entropies are key diagnostics of structure, ``nonstabilizerness,'' phase transitions, and universality in quantum many-body states. We establish an exact correspondence for quadratic fermions: for any Gaussian eigenstate, the stabilizer Rényi entropy equals the Shannon-Rényi entropy of a number-conserving free-fermion eigenstate on a doubled system, evaluated in the computational basis. Specializing to the transverse-field Ising (TFI) chain, the TFI ground-state stabilizer entropies map to the Shannon-Rényi entropies of the XX-chain ground state of length $2L$. Building on this correspondence, together with other exact identities we prove, we derive closed expressions for the stabilizer entropy at indices $\alpha=\tfrac{1}{2},2,4$ for a broad class of critical closed free-fermion systems. Each of these can be written with respect to the universal functions of the TFI chain. We further derive conformal-field-theory scaling laws for the stabilizer entropy at arbitrary Rényi index under both periodic and open boundary conditions. At $\alpha=4$, these scaling forms display a discontinuity for both open and periodic boundary conditions. Comments: VIII: 7+31 pages, 1 Figure Subjects: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2509.10700 [quant-ph] (or arXiv:2509.10700v4 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2509.10700 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Lett. 137, 090403 (2026) Related DOI : https://doi.org/10.1103/2frt-tdg9 Focus to learn more DOI(s) linking to related resources Submission history From: Eddy Ariel Ramirez Trino [ view email ] [v1] Fri, 12 Sep 2025 21:32:10 UTC (20 KB) [v2] Fri, 3 Oct 2025 21:02:08 UTC (21 KB) [v3] Fri, 22 May 2026 14:15:09 UTC (130 KB) [v4] Fri, 28 Aug 2026 06:19:38 UTC (130 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-09 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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