2019/10/31 by Xiao-Ming Lu, Zhihao Ma, Chengjie Zhang
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Coherence (philosophical gambling strategy) #Cramér–Rao bound #Estimation theory #Fisher information #Geometric mean #Geometry #Harmonic mean #Mathematics #Mean squared error #Metrology #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum capacity #Quantum information #Quantum mechanics #Quantum metrology #Quantum network #Scalar (mathematics) #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1103/physreva.101.022303
published as Phys. Rev. A 101, 022303 (2020) · 9 pages, 2 figures, 1 table. Accepted version
openalex created_date 2019/10/18 · arxiv created 2020/02/05 · openalex publication_date 2020/02/05 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/05
In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of permissible error combinations. By defining the weighted f-mean of estimation error and quantum Fisher information, we derive various quantum Cram'er-Rao bounds on mean error in a very general form and give their refined versions with complex quantum Fisher information matrices. We show that the geometric- and harmonic-mean quantum Cram'er-Rao bounds can help to reveal a larger forbidden region of estimation error for a complex signal in coherent light accompanied by a thermal background than just using the ordinary arithmetic-mean version. Moreover, we show that the f-mean quantum Fisher information can be considered as information-theoretic quantities and is useful in quantifying asymmetry and coherence as quantum resources.