2017/10/31 by Mark Bradshaw, Ping Koy Lam, Syed M. Assad · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Cramér–Rao bound #Gaussian #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Physics #Quadrature (astronomy) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Separable space #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1103/physreva.97.012106
published as Phys. Rev. A 97, 012106 (2018) · 12 pages, 2 figures
openalex publication_date 2018/01/09 · arxiv created 2018/01/19 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Holevo Cram'er-Rao bound is a lower bound on the sum of the mean-square error of estimates for parameters of a state. We provide a method for calculating the Holevo Cram'er-Rao bound for estimation of quadrature mean parameters of a Gaussian state by formulating the problem as a semidefinite program. In this case, the bound is tight; it is attained by purely Gaussian measurements. We consider the example of a symmetric two-mode squeezed thermal state undergoing an unknown displacement on one mode. We calculate the Holevo Cram'er-Rao bound for joint estimation of the conjugate parameters for this displacement. The optimal measurement is different depending on whether the state is entangled or separable.