The DOI matches its Crossref record; 35 of the 35 references it cites were found in a registry or an index.
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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“surement scheme, the uncertainty in the estimation of a parameter is limited by the Cramér-Rao bound, which is proportional to the inverse of the square root of the so-called Fisher information (FI) [5–7].”
BackgroundMethodInfluentialQuantum-mechanical noise in an interferometer
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Phase diffusion of light immersed in quantum tides: Open quantum system approach
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Experimental Joint Estimation of Phase and Phase Diffusion Via Deterministic Bell Measurements
Wang, B., Mi, M., Wang, H., Xie, Q., & Zhang, L. (2025) · Advanced Science · doi:10.1002/advs.202518375
General framework for estimating the ultimate precision limit in Bayesian quantum metrology
Escher, B. M. (2026) · Physical Review A · doi:10.1103/j245-wrkp
Self-citationPrecision limit under weak coupling with an ancillary qubit
Chen, P., & Jing, J. (2026) · Physical Review A · doi:10.1103/my6j-77x2 · Cited by 1
“A conventional quantum estimation protocol [2, 3, 5] consists of (1) preparing the probe into a resource state, (2) encoding the to-be-estimated parameter into the probe state, (3) performing measurements or detections on the probe to extract parametric information, and (4) processing the outcomes…”
Squeezing Enhanced Two Phase Estimation With N Particle W States
Zhang, H., Yin, G., Xia, Y., He, B., Zhang, X., Chang, S., & Ye, W. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.70426
“To rigorously quantify the ultimate precision bound under photon loss, we adopt a purification-based variational approach [ 40 ].”
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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