{"title":"The Cramér-Rao approach and global quantum estimation of bosonic states","authors":"Masahito Hayashi, Yingkai Ouyang","doi":"arxiv-2409.11842","DOIUrl":null,"url":null,"abstract":"Quantum state estimation is a fundamental task in quantum information theory,\nwhere one estimates real parameters continuously embedded in a family of\nquantum states. In the theory of quantum state estimation, the widely used\nCram\\'er Rao approach which considers local estimation gives the ultimate\nprecision bound of quantum state estimation in terms of the quantum Fisher\ninformation. However practical scenarios need not offer much prior information\nabout the parameters to be estimated, and the local estimation setting need not\napply. In general, it is unclear whether the Cram\\'er-Rao approach is\napplicable for global estimation instead of local estimation. In this paper, we\nfind situations where the Cram\\'er-Rao approach does and does not work for\nquantum state estimation problems involving a family of bosonic states in a\nnon-IID setting, where we only use one copy of the bosonic quantum state in the\nlarge number of bosons setting. Our result highlights the importance of caution\nwhen using the results of the Cram\\'er-Rao approach to extrapolate to the\nglobal estimation setting.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11842","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Quantum state estimation is a fundamental task in quantum information theory,
where one estimates real parameters continuously embedded in a family of
quantum states. In the theory of quantum state estimation, the widely used
Cram\'er Rao approach which considers local estimation gives the ultimate
precision bound of quantum state estimation in terms of the quantum Fisher
information. However practical scenarios need not offer much prior information
about the parameters to be estimated, and the local estimation setting need not
apply. In general, it is unclear whether the Cram\'er-Rao approach is
applicable for global estimation instead of local estimation. In this paper, we
find situations where the Cram\'er-Rao approach does and does not work for
quantum state estimation problems involving a family of bosonic states in a
non-IID setting, where we only use one copy of the bosonic quantum state in the
large number of bosons setting. Our result highlights the importance of caution
when using the results of the Cram\'er-Rao approach to extrapolate to the
global estimation setting.