Multi-Parameter Multi-Critical Metrology of the Dicke Model
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Quantum Physics arXiv:2603.03451 (quant-ph) [Submitted on 3 Mar 2026] Title:Multi-Parameter Multi-Critical Metrology of the Dicke Model Authors:Luca Previdi, Yilun Xu, Qiongyi He, Matteo G. A. Paris View a PDF of the paper titled Multi-Parameter Multi-Critical Metrology of the Dicke Model, by Luca Previdi and 3 other authors View PDF HTML (experimental) Abstract:Critical quantum metrology exploits the hypersensitivity of quantum systems near phase transitions to achieve enhanced precision in parameter estimation. While single-parameter estimation near critical points is well established, the simultaneous estimation of multiple parameters, which is essential for practical sensing applications, remains challenging. This difficulty arises from sloppiness, a phenomenon that typically renders the QFIM singular or nearly singular. In this work, we demonstrate that multiparameter critical metrology is not only feasible but can also retain divergent precision scaling, provided one accepts a trade-off in the scaling exponent. Using the GS of the single-cavity DM, we show that two Hamiltonian parameters can be simultaneously estimated with a scalar variance bound scaling as the square root of the critical parameter. This overcomes the inherent sloppiness by leveraging higher-order contributions to the QFIM. To recover the optimal quadratic scaling, we introduce the DD with photon hopping. In this model, a triple point in the phase diagram enables the simultaneous closure of two excitation gaps, which effectively increases the rank of the QFIM and restores the ideal single-parameter scaling for specific parameter pairs. Furthermore, we extend our to a lossy scenario. We prove that the SSs of both the DM and the DD still support multiparameter estimation with diverging precision, exhibiting linear scaling in the DM and quadratic scaling near the triple point in the DD. Finally, we establish a connection between the derived critical scalings and the fundamental state preparation time, providing a unified framework to operationally compare different sensing strategies. Our results demonstrate that critical quantum metrology can be made robust against dissipation, paving the way for practical quantum sensors operating near phase transitions. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.03451 [quant-ph] (or arXiv:2603.03451v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.03451 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Luca Previdi [view email] [v1] Tue, 3 Mar 2026 19:06:55 UTC (502 KB) Full-text links: Access Paper: View a PDF of the paper titled Multi-Parameter Multi-Critical Metrology of the Dicke Model, by Luca Previdi and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)