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Entanglement, Nonlinear Dynamics, and the Heisenberg Limit
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We show that quantum Fisher information provides a sufficient condition to recognize multiparticle entanglement in an N qubit state. The same criterion gives a necessary and sufficient condition for sub-shot-noise phase sensitivity in the estimation of a collective rotation angle theta. The analysis therefore singles out the class of entangled states which are useful to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the nonlinear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.
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“This is a result that is now firmly established [33, 36] and that comes out in a rather natural fashion within this new framework.”
From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [36]
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“For pure states, it has been shown (e.g., by Refs. [15, 21, 22]) that equality holds if and only if the initial state is an equally weighted superposition of exactly two eigenstates of H .”
From Kind of entanglement that speeds up quantum evolution (2012) · cites this paper as [22]
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“All three approaches, therefore, have the common lower bound (2).”
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Metadata
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- Pezzé, L., & Smerzi, A.
- Affiliations
- University of Trento (IT)
- ORCID
- Smerzi, Augusto
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-03-10
- Volume
- 102
- Issue
- 10
- Pages
- 100401-100401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2025363053
- Cited by
- 880
- References
- 27
- Citations by year
- 2026: 49 · 2025: 66 · 2024: 62 · 2023: 56 · 2022: 61 · 2021: 67 · 2020: 59 · 2019: 47 · 2018: 57 · 2017: 56 · 2016: 60 · 2015: 45 · 2014: 56 · 2013: 38 · 2012: 46
- FWCI
- 36.17
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum Fisher information, multipartite entanglement, Heisenberg limit, quantum metrology, nonlinear dynamics, entanglement generation, Bose-Einstein condensate, trapped ions, quantum sensing
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.
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