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Quantum Metrological Limits via a Variational Approach
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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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Self-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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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