On the philosophy of Cramér-Rao-Bhattacharya inequalities in quantum statistics.

DOI10.1007/s13171-020-00216-1zbMath1471.81032OpenAlexW3093560189MaRDI QIDQ2051006

Yanyan Li

Publication date: 1 September 2021

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.312.9738

zbMATH Keywords

uncertainty principlegeneralized measurementcovariance matrix of unbiased estimatorsCramér-Rao-Bhattacharya boundCramér-Rao-Bhattacharya tensorfinite level quantum systemFisher information formFisher map

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Topological spaces and generalizations (closure spaces, etc.) (54A05) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum measurement theory, state operations, state preparations (81P15) Vector-valued measures and integration (46G10) Measures of information, entropy (94A17) Statistical aspects of information-theoretic topics (62B10) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum state estimation, approximate cloning (81P50) Quantum entropies (81P17) Uncertainty relations, also entropic (81S07)

Cites Work

• A Mathematical Theory of Communication
• Quantum detection and estimation theory
• Coding theorems of classical and quantum information theory.
• Quantum noise
• Information theoretic inequalities
• Statistical distance and the geometry of quantum states
• Locally Best Unbiased Estimates
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