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

Fiderer, Lukas J; Tufarelli, Tommaso; Adesso, Gerardo; Piano, Samanta

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Authors

Lukas J Fiderer



Abstract

The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the density matrix. In this paper, we derive general expressions for the quantum Fisher information matrix which bypass matrix diagonalization and do not require the expansion of operators on an orthonormal set of states. Additionally, we can tackle density matrices of arbitrary rank. The methods presented here simplify analytical calculations considerably when, for example, the density matrix is more naturally expressed in terms of non-orthogonal states, such as coherent states. Our derivation relies on two matrix inverses which, in principle, can be evaluated analytically even when the density matrix is not diagonalizable in closed form. We demonstrate the power of our approach by deriving novel results in the timely field of discrete quantum imaging: the estimation of positions and intensities of incoherent point sources. We find analytical expressions for the full estimation problem of two point sources with different intensities, and for specific examples with three point sources. We expect that our method will become standard in quantum metrology.

Citation

Fiderer, L. J., Tufarelli, T., Adesso, G., & Piano, S. (2021). General Expressions for the Quantum Fisher Information Matrix with Applications to Discrete Quantum Imaging. PRX Quantum, 2(2), Article 020308. https://doi.org/10.1103/prxquantum.2.020308

Journal Article Type Article
Acceptance Date Apr 1, 2021
Online Publication Date Apr 20, 2021
Publication Date Apr 20, 2021
Deposit Date Apr 15, 2021
Publicly Available Date Mar 28, 2024
Journal PRX Quantum
Print ISSN 2691-3399
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 2
Issue 2
Article Number 020308
DOI https://doi.org/10.1103/prxquantum.2.020308
Public URL https://nottingham-repository.worktribe.com/output/5467589
Publisher URL https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.020308

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