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Fisher information and multiparticle entanglement
Open accessAbstract
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\overline{F}$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\overline{F}$ is able to detect certain bound entangled states.
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“As a result, the bound could be valid for non Markovian dynamics as long as they admit a representation in terms of a CP map [38].”
From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [38]
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“Apart from quantum metrology, the QFI also connects to other aspects of quantum physics, such as quantum phase transition [18][19][20] and entanglement witness [21,22].”
From Quantum Fisher information matrix and multiparameter estimation (2020) · cites this paper as [21]
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Research works printed but not linked: 1
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Sorted by citations
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
“The inequalities (48) have been generalized to arbitrary spin systems (Vitagliano et al., 2014, 2011) and to systems of fluctuating numbers of particles (Hyllus et al., 2012b).”
BackgroundSelf-citationQuantum 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
Quantum Fisher information matrix and multiparameter estimation
Liu, J., Yuan, H., Lu, X.-M., & Wang, X. (2020) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/ab5d4d · Cited by 802
Quantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 672
Metadata
- Authors
- Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., & Smerzi, A.
- Affiliations
- University of the Basque Country (ES)
- University of Gdańsk (PL)
- Max Planck Institute of Quantum Optics (DE)
- University of Trento (IT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-02-16
- Volume
- 85
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2041209858
- Cited by
- 593
- References
- 80
- Citations by year
- 2026: 44 · 2025: 80 · 2024: 74 · 2023: 52 · 2022: 38 · 2021: 57 · 2020: 43 · 2019: 46 · 2018: 32 · 2017: 33 · 2016: 32 · 2015: 31 · 2014: 16 · 2013: 9 · 2012: 6
- FWCI
- 19.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- INO Open Portal (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- 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 › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- Fisher information, multipartite entanglement, quantum phase estimation, quantum interferometry, shot-noise limit, entanglement detection, bound entangled states, quantum metrology
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