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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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
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On the mathematical foundations of theoretical statistics
Fisher, R. A. (1922) · Philosophical Transactions of the Royal Society of London Series A Containing Papers of a Mathematical or Physical Character · doi:10.1098/rsta.1922.0009 · Cited by 4,055
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894
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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
Caves, C. M. (1981) · Physical Review D · doi:10.1103/physrevd.23.1693 · Cited by 3,202
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
“Equation (133) suggests to search for the minimum of FQ1⁄2jψ θ i over all purifications of ρ̂θ (Escher, de Matos Filho, and Davidovich, 2011; Escher et al., 2012).”
BackgroundQuantum Limits in Optical Interferometry
Demkowicz-Dobrzański, R., Jarzyna, M., & Kołodyński, J. (2015) · Progress in optics · doi:10.1016/bs.po.2015.02.003 · Cited by 562
“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).”
MethodQuantum Speed Limit for Physical Processes
Taddei, M. M., Escher, B. M., Davidovich, L., & de Matos Filho, R. L. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.050402 · Cited by 509
Self-citationPolino, E., Valeri, M., Spagnolo, N., & Sciarrino, F. (2020) · AVS Quantum Science · doi:10.1116/5.0007577 · Cited by 443
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 328
“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…”
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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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