2015/01/31 by Jing Liu, Jie Chen, Xiao-Xing Jing +1 · 3 citations
Computer Science · Physics and Astronomy · #Class (philosophy) #Construct (python library) #Derivative (finance) #Least-squares function approximation #Logarithm #Logarithmic derivative #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Second derivative #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/49/27/275302
published as J. Phys. A: Math. Theor. 49, 275302 (2016) · 12 pages, no figure
arxiv created 2016/05/24 · openalex publication_date 2016/05/24 · arxiv updated 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anti-commutators. This method has originated from the Lyapunov representation and would be very useful for cases where the anti-commutators among the state and its partial derivative exhibit periodic properties. As an application, we discuss a class of states whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation scenarios.