Sufficient support size of measurements for quantum estimation
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Quantum Physics arXiv:2604.21323 (quant-ph) [Submitted on 23 Apr 2026] Title:Sufficient support size of measurements for quantum estimation Authors:Koichi Yamagata View a PDF of the paper titled Sufficient support size of measurements for quantum estimation, by Koichi Yamagata View PDF HTML (experimental) Abstract:In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set $\Omega$ and $\hat{\theta}:\Omega\to\mathbb{R}^{d}$ is a classical estimator map. Since the number of outcomes $\left|\Omega\right|$ is a priori unbounded, the space of admissible POVMs is vast, which makes the search for optimal estimators difficult. In this paper, for the minimization of the weighted trace of the mean squared error among locally unbiased estimators, we prove that it suffices to consider POVMs with at most $\left({\rm dim}\,\mathcal{H}\right)^{2}+d(d+1)/2-1$ outcomes, and that an optimal measurement can be chosen to be rank-one. For the minimization of the average weighted trace of the mean squared error in Bayesian estimation, we show that it suffices to consider POVMs with at most $\left( {\rm dim}\, \mathcal{H}\right)^{2}$outcomes, and again an optimal POVM can be taken to be rank-one. Furthermore, when the model admits a real sufficient subalgebra, we show that the $\left( {\rm dim}\, \mathcal{H} \right)^{2}$ term in the above support-size bounds can be reduced in both the locally unbiased and Bayesian settings. These bounds substantially reduce the search space for optimal measurements and justify restricting numerical optimization to rank-one POVMs with finitely many outcomes. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.21323 [quant-ph] (or arXiv:2604.21323v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.21323 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Koichi Yamagata [view email] [v1] Thu, 23 Apr 2026 06:26:07 UTC (11 KB) Full-text links: Access Paper: View a PDF of the paper titled Sufficient support size of measurements for quantum estimation, by Koichi YamagataView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)