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Quantum covariance, quantum Fisher information and the uncertainty principle

Paolo Gibilisco, Fumio Hiai, Dėnes Petz

In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given hereconsiderably simplifies the previously proposed proofs and leads to more general inequalities.

arXiv:0712.1208Dec 7, 20076 citations

On Fisher Information of Quantum Statistical Models

Hiroshi Nagaoka

WORLD SCIENTIFIC eBooksFeb 1, 200527 citations

Direct approach to quantum extensions of Fisher information

Ping Chen, Shunlong Luo

Frontiers of MathematicsJul 1, 200722 citations

Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

Paolo Gibilisco, Fumio Hiai, Dėnes Petz

In this paper, the relation between quantum covariances and quantum Fisher informations is studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given here considerably simplifies the previously proposed proofs and leads to more general inequalities.

IEEE Transactions on Information TheoryJan 1, 200959 citations

Quantum Fisher Information and Uncertainty Relations

Shunlong Luo

Letters in Mathematical PhysicsAug 1, 200094 citations

Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors

Ievgen I. Arkhipov, Franco Nori, Şahin Kaya Özdemir

Non-Hermitian systems have attracted considerable interest over the last few decades due to their unique spectral and dynamical properties not encountered in Hermitian counterparts. An intensely debated question is whether non-Hermitian systems, described by pseudo-Hermitian Hamiltonians with real spectra, can offer enhanced sensitivity for parameter estimation when they are operated at or close to exceptional points. However, much of the current analysis and conclusions are based on mathematical formalism developed for Hermitian quantum systems, which is questionable when applied to pseudo-Hermitian Hamiltonians, whose Hilbert space is intrinsically nonflat. Here, we develop a covariant formulation of quantum Fisher information (QFI) defined on the deformed Hilbert space of pseudo-Hermitian Hamiltonians. This covariant framework ensures the preservation of the state norm and enables a consistent treatment of parameter sensitivity. We further show that the covariant QFI of pseudo-Hermitian systems is dual to the ordinary QFI of corresponding Hermitian systems. Importantly, this correspondence naturally imposes an upper bound on the covariant QFI and allows one to identify optimal projections which saturate the corresponding classical Fisher information to this ultimate limit. The developed framework also enables to set the criteria under which pseudo-Hermitian sensors can exhibit an advantage over their Hermitian counterparts of the same dimensionality.Non-Hermitian systems have attracted considerable interest over the last few decades due to their unique spectral and dynamical properties not encountered in Hermitian counterparts. An intensely debated question is whether non-Hermitian systems, described by pseudo-Hermitian Hamiltonians with real spectra, can offer enhanced sensitivity for parameter estimation when they are operated at or close to exceptional points. However, much of the current analysis and conclusions are based on mathematical formalism developed for Hermitian quantum systems, which is questionable when applied to pseudo-Hermitian Hamiltonians, whose Hilbert space is intrinsically nonflat. Here, we develop a covariant formulation of quantum Fisher information (QFI) defined on the deformed Hilbert space of pseudo-Hermitian Hamiltonians. This covariant framework ensures the preservation of the state norm and enables a consistent treatment of parameter sensitivity. We further show that the covariant QFI of pseudo-Hermitian systems is dual to the ordinary QFI of corresponding Hermitian systems. Importantly, this correspondence naturally imposes an upper bound on the covariant QFI and allows one to identify optimal projections which saturate the corresponding classical Fisher information to this ultimate limit. The developed framework also enables to set the criteria under which pseudo-Hermitian sensors can exhibit an advantage over their Hermitian counterparts of the same dimensionality.

arXiv:2506.09763Physical Review LettersJan 27, 20264 citations

On Covariance and Quantum Fisher Information

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On Covariance and Quantum Fisher Information

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