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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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“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]
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]
In the citing paper
“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]
In the citing paper
“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]
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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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