The Most Informative Cram\'er--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes

Quantum Physics arXiv:2511.14950 (quant-ph) [Submitted on 18 Nov 2025] Title:The Most Informative Cramér--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes Authors:Simon K. Yung, C. M. Yung, Lorcán O. Conlon, Syed M. Assad View a PDF of the paper titled The Most Informative Cram\'er--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes, by Simon K. Yung and 3 other authors View PDF HTML (experimental) Abstract:Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of determining the minimum achievable estimation error is a central task of multiparameter quantum metrology. For estimating parameters encoded in pure quantum states, the ultimate limit is known, but is given by the solution of a non-trivial minimisation problem. We present a new expression for the achievable bound for two-parameter estimation with pure states that is considerably simpler. We also determine the optimal measurements, completing the problem of two-parameter estimation with pure state probes. To demonstrate the utility of our result, we determine the precision limit for estimating displacements using grid states. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.14950 [quant-ph] (or arXiv:2511.14950v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.14950 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Simon K Yung [view email] [v1] Tue, 18 Nov 2025 22:15:14 UTC (103 KB) Full-text links: Access Paper: View a PDF of the paper titled The Most Informative Cram\'er--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes, by Simon K. Yung and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?)