The DOI matches its Crossref record; 41 of the 42 references it cites were found in a registry or an index.
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
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“It has been proved that, in the presence of losses or other types of noise, no two-mode quantum state can beat the standard limit by more than just a constant factor in the limit of large N12131415.”
From Photonic polarization gears for ultra-sensitive angular measurements (2013) · cites this paper as [13]
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“The optimal bound (see Table 1) corresponds to h with non-zero elements . This bound is asymptotically equally tight to the best bounds known in the literature383940, proving again that CE method despite its simplicity is able to provide powerful results in a straightforward manner.”
From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [40]
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“In this case, F Q ( t ) = 4 〈 ∆ ˆ H 2 ( t ) 〉 / ℏ 2 [49], where 〈 ∆ ˆ H 2 ( t ) 〉 is the variance in the initial state of a Hermitian operator ˆ H ( t ) defined as”
From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [49]
In the citing paper
“Then with eq. (8) and the fact that the Fisher information obeys F ≤ N 2 [34, 35], the limit on the speed of evolution imposes the persistence of the standard scaling D f ∼ 1 / √ N no matter how weak the dephasing rate.”
From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [35]
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“Most importantly, the above bound, is exactly the same as the one derived by Escher et al.40 or by the CE method, where the minimum in equation (19) corresponds to .”
From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [40]
In the citing paper
“Unfortunately, both the theory29303132333435 and experiments3637 confirmed the fragility of the above schemes when noise sources such as decoherence are considered, and it has been rigorously shown for particular models that asymptotically with respect to N, even infinitesimally small noise turns HS into SS, so that the quantum gain amounts to a constant factor improvement383940.”
From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [40]
In the citing paper
“Even though the minimization over purification method40 yields in principle a tight bound, in practice there is no effective algorithm to find a global minimum, and the only way to convince oneself that one has achieved the global minimum is again to show that the theoretical lower bound on estimation uncertainty coincides with the performance of a particular estimation strategy.”
From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [40]
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Citations
Cites
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
Mathematical Methods of Statistics.
Geary, R. C., & Cramer, H. L. (1947) · The Economic Journal · doi:10.2307/2226151 · Cited by 6,095
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776
Quantum-mechanical noise in an interferometer
Caves, C. M. (1981) · Physical Review D · doi:10.1103/physrevd.23.1693 · Cited by 3,202
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,160
Quantum Detection and Estimation Theory
(1976) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6017-5 · Cited by 2,712
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440
Cited by
Sorted by citations
Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E., & Schmidt, P. O. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.637 · Cited by 2,385
Colloquium : Quantum coherence as a resource
Streltsov, A., Adesso, G., & Plenio, M. B. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.041003 · Cited by 1,878
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
Quantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/42/424006 · Cited by 862
The elusive Heisenberg limit in quantum-enhanced metrology
Demkowicz-Dobrzański, R., Kołodyński, J., & Guţă, M. (2012) · Nature Communications · doi:10.1038/ncomms2067 · Cited by 773
Metadata
- Authors
- Escher, B. M., de Matos Filho, R. L., & Davidovich, L.
- Affiliations
- Universidade Federal do Rio de Janeiro (BR)
- Corresponding author
- Escher, B. M.
- Venue
- Nature Physics
- Published
- 2011-03-27
- Volume
- 7
- Issue
- 5
- Pages
- 406-411
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W2007948277
- Cited by
- 928
- References
- 42
- Citations by year
- 2026: 56 · 2025: 74 · 2024: 76 · 2023: 52 · 2022: 50 · 2021: 62 · 2020: 78 · 2019: 66 · 2018: 60 · 2017: 76 · 2016: 68 · 2015: 67 · 2014: 61 · 2013: 46 · 2012: 30
- FWCI
- 42.14
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature Physics (publishedVersion)
- arXiv (Cornell University) (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-enhanced sensing, noisy quantum systems, quantum Fisher information, dephasing, atomic spectroscopy, adaptive feedback, parameter estimation
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