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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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Yang, H.-Y., Zhang, K., Wang, X.-H., & Shi, H. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.085410 · Cited by 20
Metrologically resourceful multipartite entanglement under quantum many-body effects
Khalid, U., Rehman, J. U., & Shin, H. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abd893 · Cited by 19
Tian, M., Xiang, Y., Sun, F.-X., Fadel, M., & He, Q. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.18.024065 · Cited by 20
Classification of four-qubit entangled states via machine learning
Vintskevich, S., Bao, N., NOMEROTSKI, A., Stankus, P. W., & Grigoriev, D. A. (2023) · Physical Review A · doi:10.1103/physreva.107.032421 · Cited by 23
Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering
Hales, J., Bajpai, U., Liu, T., Baykusheva, D., Li, M., Mitrano, M., & Wang, Y. (2023) · Nature Communications · doi:10.1038/s41467-023-38540-3 · Cited by 19
“(14) does not automatically impose SU(2), translational, and point-group symmetries, which are challenging to implement in sizeable fermionic systems.”
InfluentialQuantum parameter estimation of non-Hermitian systems with optimal measurements
Yu, X., & Zhang, C. (2023) · Physical Review A · doi:10.1103/physreva.108.022215 · Cited by 22
Squeezing and quantum approximate optimization
Santra, G. C., Jendrzejewski, F., Hauke, P., & Egger, D. J. (2024) · Physical Review A · doi:10.1103/physreva.109.012413 · Cited by 27
“A sufficient condition for (k + 1)-partite entanglement stems from the quantum Fisher information FQ: a state reaching FQ[ρn,O] > (sk2 + r2)—where s = bn/kc denotes the integer division of n by k, and r is the remainder—is at least (k + 1)partite entangled [34, 35].”
BackgroundInfluentialQuantum Metrology Assisted by Machine Learning
Huang, J., Zhuang, M., Zhou, J., Shen, Y., & Lee, C. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300329 · Cited by 21
Metrology and multipartite entanglement in measurement-induced phase transition
Fresco, G. D., Spagnolo, B., Valenti, D., & Carollo, A. C. M. (2024) · Quantum · doi:10.22331/q-2024-04-30-1326 · Cited by 19
“The QFI is a witness of multi-partite entanglement [31, 32, 33, 34], as well known from quantum metrology [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49].”
BackgroundMethod
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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