Quantum Fisher information matrix and multiparameter estimation
By Jing Liu, Haidong Yuan, Xiao-Ming Lu, Xiaoguang Wang. Journal of Physics A: Mathematical and Theoretical, 2019
863 citations recorded by the source corpus.
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér–Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9bb5bf567d8bcef47326edb29bdd28a4b742327f
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Citations in the corpus
- Estimating the gradient and higher-order derivatives on quantum hardware (2020, methodology): “[15] Jing Liu, Haidong Yuan, Xiao-Ming Lu, and Xiaoguang Wang.”