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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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“These quantities become useful because (i) they are experimentally accessible, and (ii) it is possible to derive bounds for f Q (or nQFI) that can only be reached by certain classes of multipartite-entangled states [8,9,53].”
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Quantum Fisher information and spin squeezing in one-axis twisting model
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“This insight has inspired a series of studies that refine and extend the criterion to account for states of given entanglement depth [14, 15], states characterized by Young diagrams [19], networked states in distributed sensing [23], and situations where H is nonlinear [24].”
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“Kuantum Fisher Bilgisinin, genel bir çok taraflı dolanıklık ölçütü bulunabileceği düşünülmekte ve bu doğrultuda çalışmalar sürmektedir [32].”
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“…and quantum physics: quantum Fisher information (QFI) [24, 25] as a potent witness of multipartite entanglement [26–30], and quantum delocalization that is a captivating phenomenon underpinning a plethora of cutting-edge quantum effects such as ther-malization, scrambling, and hydrodynamics in…”
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Elghaayda, S., Ali, A., Abd‐Rabbou, M. Y., Mansour, M., & Al-Kuwari, S. M. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14175-0 · Cited by 17
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“Although entanglement is recognized as a fundamental resource for phase estimation [38, 39], is remarkable to note that phase sensitivity is observed even in the full dephasing regime, whereby the entanglement is always zero, even for the encoded states.”
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“Moreover, for a fixed N , the value of the FI may raise by increasing the amount of particle entanglement in the probe [11,12].”
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Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain
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Quantum Wasserstein distance based on an optimization over separable states
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BackgroundGeneralized-mean Cramér-Rao bounds for multiparameter quantum metrology
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Entanglement criteria based on quantum Fisher information
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Quantifying computational advantage of Grover’s algorithm with the trace speed
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Self-citationNonlocal operation enhanced entanglement detection and classification
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Quantum-dynamical phase transition and Fisher information in a non-Hermitian Bose-Hubbard dimer
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“Nonetheless, one still is able to identify areas that ¯ F J y > 1, though slightly, which signals passing the SQL as it is expected from a graph state [27] as well as a multiparticle entangled state [49].”
Electric field modified quantum entropic measures of particle in a spherical box
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Liu, X., Du, Z. Z., Cheng, W. W., & Liu, J. (2015) · Solid State Communications · doi:10.1016/j.ssc.2015.04.007 · Cited by 11
Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model
Lambert, J., & Sørensen, E. S. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.224401 · Cited by 11
Quantum Fisher information and spin squeezing in one-axis twisting modelPreprint
Zhong, W., Liu, J., Ma, J., & Wang, X. (2016) · Cited by 12
The application of quantum coherence as a resource
刘, S.-Y. 思. L., & 范, H. 桁. F. (2023) · Chinese Physics B · doi:10.1088/1674-1056/acfa85 · Cited by 12
Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
Bhunia, A., Bera, S., Biswas, I., Chattopadhyay, I., & Sarkar, D. (2024) · Physical Review A · doi:10.1103/physreva.109.052211 · Cited by 10
Quantum metrology of rotations with mixed spin states
Serrano-Ensástiga, E., Chryssomalakos, C., & Martin, J. (2025) · Physical Review A · doi:10.1103/physreva.111.022435 · Cited by 12
Factorization dynamics between quantum Fisher information and quantum coherence
Zhao, X., Yu, X., Li, L., Zhou, W., & Zhang, C. (2025) · Science Advances · doi:10.1126/sciadv.adv8132 · Cited by 10
“The QFI has many applications in quantum information theory, such as uncertainty relations ( 15 , 16 ), entanglement detection ( 17 – 19 ), characterizing the non-Markovianity of open systems ( 20 – 22 ), and determining the optimal measurements for estimating parameters ( 23 – 25 ).”
Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains
Köylüoğlu, N. U., Maskara, N., Feldmeier, J., & Lukin, M. D. (2025) · Physical Review Letters · doi:10.1103/5qhh-322q · Cited by 19
“In particular, a QFI density F Q /L > m implies at least ( m +1)- body entanglement [69], such that F Q /L > 1 indicates non-classical correlations and F Q /L = L corresponds to a maximally entangled GHZ state, which saturates the Heisenberg limit.”
BackgroundExperimental violation of the local realism for four-qubit Dicke state
Zhao, Y., Wu, Y.-C., Xiang, G., Li, C., & Guo, G. (2015) · Optics Express · doi:10.1364/oe.23.030491 · Cited by 10
Continuous-variable multipartite vibrational entanglement
Abdi, M. (2021) · Physical Review A · doi:10.1103/physreva.103.043520 · Cited by 10
Measurement-induced multipartite-entanglement regimes in collective spin systems
Poggi, P. M., & Muñoz-Arias, M. H. (2024) · Quantum · doi:10.22331/q-2024-01-18-1229 · Cited by 10
“See [52] for a detailed analysis on F Q as a multipartite entan-glement witness.”
BackgroundQuantum Fisher information-based detection of genuine tripartite entanglement
Yang, L.-M., Sun, B.-Z., Chen, B., Fei, S.-M., & Wang, Z. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02766-7 · Cited by 9
“This special type of multipartite entanglement plays an important role in various quantum information processing tasks such as in the context of extreme spin squeezing [3] and highly sensitive metrological tasks [4, 5].”
BackgroundNonclassical properties and quantum resources of hierarchical photonic superposition states
Volkoff, T. J. (2015) · Journal of Experimental and Theoretical Physics · doi:10.1134/s1063776115110187 · Cited by 10
On the quantum spin glass transition on the Bethe lattice
Mossi, G., Parolini, T., Pilati, S., & Scardicchio, A. (2017) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/aa5286 · Cited by 10
Tutorial: Extracting entanglement signatures from neutron spectroscopy
Scheie, A. O., Laurell, P., Simeth, W., Dagotto, E. R., & Tennant, D. M. (2024) · Materials Today Quantum · doi:10.1016/j.mtquan.2024.100020 · Cited by 9
“The relationship between QFI and multipartite entan-glement is where m is an integer and is the lower bound on entanglement depth, and h min/max are the minimal and maximal eigenvalues of the local operators building up O [19, 20, 23, 24].”
BackgroundMetrological usefulness of entanglement and nonlinear Hamiltonians
Imai, S., Smerzi, A., & Pezzè, L. (2025) · Physical Review A · doi:10.1103/physreva.111.l020402 · Cited by 9
Self-citationEntanglement Witness for Indistinguishable Electrons Using Solid-State Spectroscopy
Liu, T., Xu, L., Liu, J., & Wang, Y. (2025) · Physical Review X · doi:10.1103/physrevx.15.011056 · Cited by 10
“Many-body entanglement can be witnessed by two-point correlations such as the two-tangle [92] and spin QFI [38], which are accessible via solid-state spectroscopy techniques [40].”
Amplified multipartite entanglement witnessed in a quantum critical metal
Fang, Y., Mahankali, M., Wang, Y., Chen, L., Hu, H., Paschen, S. B., & Qimiao Si, A. (2025) · Nature Communications · doi:10.1038/s41467-025-57778-7 · Cited by 9
“Here, g is taken to be 2 .”
Sensitivity of quantum magnetic sensing
Lei, L., Wu, T., & Guo, H. M. (2025) · National Science Review · doi:10.1093/nsr/nwaf129 · Cited by 9
Spin Dynamics in the Dirac U(1) Spin Liquid YbZn 2 GaO 5
Wu, H. C. H., Pratt, F. L., Huddart, B. M., Chatterjee, D., Goddard, P., Singleton, J., Prabhakaran, D., & Blundell, S. J. (2025) · Physical Review Letters · doi:10.1103/l93v-f576 · Cited by 9
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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