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Quantum Metrological Limits via a Variational Approach
Open accessAbstract
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.
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“On the other hand, it has also been shown in [46] that the Bures length of a geodesic joining two density operators ˆ ρ 1 and ˆ ρ 2 is arccos √ F B (ˆ ρ 1 , ˆ ρ 2 ) [48], which defines a natural distance D between the two states.”
From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [48]
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Cited by
Sorted by citations
Quantum metrology with nonclassical states of atomic ensembles
Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R., & Treutlein, P. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035005 · Cited by 1,864
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“Since upper bounds on QFI translate to lower bounds on estimation uncertainty this approach proved useful in deriving bounds in quantum metrology in presence of decoherence (Escher et al., 2012, 2011).”
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Open-system dynamics of entanglement:a key issues review
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“Stabilization techniques may help increase the robustness of quantum communication and information processing tasks and may also be applied to quantum metrology where the presence of decoherence tends to drive the precision in the estimation of parameters from the ultimate quantum limit (sometimes called the ‘Heisenbe…”
BackgroundSelf-citation
Metadata
- Authors
- Escher, B. M., Davidovich, L., Zagury, N., & de Matos Filho, R. L.
- Affiliations
- Universidade Federal do Rio de Janeiro (BR)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-11-09
- Volume
- 109
- Issue
- 19
- Pages
- 190404-190404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2032966202
- Cited by
- 138
- References
- 35
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 6 · 2023: 34 · 2022: 11 · 2021: 7 · 2020: 10 · 2019: 3 · 2018: 2 · 2017: 13 · 2016: 10 · 2015: 7 · 2014: 13 · 2013: 8 · 2012: 1
- FWCI
- 9.11
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum Fisher information, quantum metrology, variational methods, noisy quantum systems, phase shift estimation, phase diffusion, estimation uncertainty
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