2016/06/30 by Esteban Martinez, Esteban Martínez-Vargas, Carlos Pineda +3 · 29 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Estimation theory #Estimator #Mathematical analysis #Mathematical optimization #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum system #Statistical physics #Statistics #Upper and lower bounds #Value (mathematics) #quant-ph
paper · pdf · doi:10.1103/physreva.95.012136
published in Physical Review A 95(1) (American Physical Society) · 6 pages
openalex created_date 2016/08/23 · openalex publication_date 2017/01/27 · arxiv created 2017/02/03 · arxiv updated 2017/02/07 · openalex updated_date 2026/08/05
We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence allows one to minimize the estimation error, can only be determined if the value of the parameter is already known. A modification of the quantum Van Trees inequality, which gives a lower bound on the error in the estimation of a random parameter, is proposed. The suggested inequality allows us to assert if a particular quantum measurement, together with an appropriate estimator, is optimal. An adaptive strategy to estimate the value of a parameter, based on our modified inequality, is proposed.