Covariance and Fisher information in quantum mechanics
Open accessAbstract
Variance and Fisher information are ingredients of the Cramér-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasize that Fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
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Transversal dephasing noise is the relevant scenario whereby one can attain precision in estimation of ω0 scaling superclassically with the number of qubits, even if noise applies independently to each qubit; any superclassical advantage is lost for parallel dephasing.
“More precisely, transversal dephasing noise stands as the relevant scenario whereby one can attain a precision in the estimation of the parameter ω 0 that scales superclassically with the number of qubits, even if such noise applies independently to each qubit (while any superclassical advantage is lost in the case of parallel dephasing noise).”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [59]
The bound is useful in practical scenarios of noisy quantum metrology, especially in the case of transversal dephasing.
“The bound is useful in practical scenarios of noisy quantum metrology, especially in the case of transversal dephasing [59,60].”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [59]
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“10) which was called generalized variance in [31].”
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- Authors
- Petz, D.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2002-01-21
- Volume
- 35
- Issue
- 4
- Pages
- 929-939
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1964020044
- Cited by
- 132
- References
- 26
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 6 · 2023: 6 · 2022: 3 · 2021: 6 · 2020: 8 · 2019: 7 · 2018: 15 · 2017: 6 · 2016: 7 · 2015: 2 · 2014: 6 · 2013: 6 · 2012: 3
- FWCI
- 2.90
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Hungarian Scientific Research Fund
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- Fisher information, covariance, variance, Cramér-Rao inequality, Riemannian metrics, coarse-graining, Kullback-Leibler divergence, contrast function, scalar curvature, quantum information geometry
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