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 result is now firmly established and comes out naturally within this new framework.
“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]
For pure states, equality in the bound holds if and only if the initial state is an equally weighted superposition of exactly two eigenstates of H.
“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]
All three approaches to survival probability have the common lower bound (2).
“All three approaches, therefore, have the common lower bound (2).”
From Kind of entanglement that speeds up quantum evolution (2012) · cites this paper as [22]
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Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes
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Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom
Chalopin, T., Bouazza, C., Evrard, A., Makhalov, V., Dreon, D., Dalibard, J., Sidorenkov, L. A., & Nascimbène, S. (2018) · Nature Communications · doi:10.1038/s41467-018-07433-1 · Cited by 96 · see citing works
Metrological Nonlinear Squeezing Parameter
Gessner, M., Smerzi, A., & Pezzè, L. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.090503 · Cited by 93 · see citing works
Self-citationSpin-Mixing Interferometry with Bose-Einstein Condensates
Gabbrielli, M., Pezzè, L., & Smerzi, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.163002 · Cited by 91 · see citing works
Self-citationQuantum Fisher Information from Randomized Measurements
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Quantum geometry in quantum materials
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Optimal probe states for the estimation of Gaussian unitary channels
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Quantum synchronisation enabled by dynamical symmetries and dissipation
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Origin of the slow growth of entanglement entropy in long-range interacting spin systems
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Variational quantum algorithm for estimating the quantum Fisher information
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Sub-shot-noise quantum metrology with entangled identical particles
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High-Precision Quantum-Enhanced Gravimetry with a Bose-Einstein Condensate
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Quantifying and Controlling Entanglement in the Quantum Magnet Cs2CoCl4
Laurell, P., Scheie, A. O., Mukherjee, C. J., Koza, M. M., Enderle, M., Tylczyński, Z., Okamoto, S., Coldea, R., Tennant, D. M., & Alvarez, G. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.037201 · Cited by 77 · see citing works
- Authors
- 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 › Computer Science › Artificial Intelligence › 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
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