General Expressions for the Quantum Fisher Information Matrix with Applications to Discrete Quantum Imaging

The quantum Fisher information matrix is a central object in multiparameter estimation theory. It usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of density matrix. In this paper, we derive general that bypass and do not require expansion operators an orthonormal set states. Additionally, can tackle matrices arbitrary rank. presented here simplify calculations considerably when, example, more naturally expressed terms nonorthogonal states, such as coherent Our derivation relies two inverses that, principle, be evaluated analytically even when diagonalizable closed form. We demonstrate power our approach by deriving novel results timely field discrete imaging: positions intensities incoherent point sources. find full problem sources with different specific examples three expect method will become standard metrology.Received 19 December 2020Accepted 1 April 2021Corrected 2 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020308Published American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum metrologyQuantum Information