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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]
In the citing paper
“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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“For comparison, we have also displayed the results from GHZ states (black squares) and TF states (blue triangles), which owns the relative larger QFI under perfect local operation [34] and performs weaker than WS state after trace.”
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“Indeed, when 4Var Q / N > k or when QFI / N > k , one can conclude that spins in each chain exhibit at least ( k + 1)-partite entanglement [17, 42, 43].”
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Parameter estimation in n-dimensional massless scalar field
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Dissipative quantum Fisher information for a general Liouvillian parametrized process
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Characterizing the width of entanglement
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Theory of a Kaptiza-Dirac Interferometer with Cold Trapped Atoms
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BackgroundEntanglement dynamics between Ising spins and a central ancilla
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On the dissipative dynamics of entangled states in coupled-cavity quantum electrodynamics arrays
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Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials
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Nonequilibrium Effects on the Precision of Parameter Estimation
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Can multipartite entanglement be characterized by two-point connected correlation functions?
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“On the other hand, genuine multipartite entanglement is necessary to reach the maximum sensitivity in certain metrological tasks 36,50 , making strange metals interesting material candidates.”
Quantum chaos, randomness and universal scaling of entanglement in various Krylov spaces
Shi, H.-L., Smerzi, A., & Pezzè, L. (2025) · SciPost Physics · doi:10.21468/scipostphys.19.4.102 · Cited by 6
Self-citationUniversal criteria for entanglement-assisted dynamical speed enhancement
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Dynamical multipartite entanglement in a generalized Tavis-Cummings model with X Y spin interaction
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All multipartite entanglements are quantum coherences in locally distinguishable bases
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Measuring multipartite quantum correlations by thermodynamic work extraction
Yada, T., Yoshioka, N., & Sagawa, T. (2025) · Physical Review Research · doi:10.1103/s8h3-5ptz · Cited by 4
Entanglement of Local Hidden States
Fadel, M., & Gessner, M. (2022) · Quantum · doi:10.22331/q-2022-02-15-651 · Cited by 4
“This bound implies widely used entanglement criteria for w-producible states [45, 44] when the information provided by h is ignored and demonstrates, in particular, that fully separable systems with (w, h) = (1, N) are limited to a sensitivity at the shot-noise limit FQ[ρ, Jz] ≤ N whereas genuine N -partite entangled…”
BackgroundEntanglement of particles versus entanglement of fields: Independent quantum resources
Sperling, J., & Agudelo, E. (2023) · Physical Review A · doi:10.1103/physreva.107.042420 · Cited by 4
Abdel‐Khalek, S., Algarni, M., Marín, M., & Berrada, K. (2023) · Optical and Quantum Electronics · doi:10.1007/s11082-023-05504-2 · Cited by 4
“Lately, it has been shown that quantum FI is largely related to quantum entanglement (Hyllus et al. 2012; Tóth 2012; Berrada et al. 2012; Berrada 2013).”
BackgroundQuantum metrology enhanced by the XY spin interaction in a generalized Tavis-Cummings model
Su, Y., Lu, W., & Shi, H. (2024) · Physical Review A · doi:10.1103/physreva.109.042614 · Cited by 4
Coherence-Enhanced Single-Qubit Thermometry out of Equilibrium
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“For the scope of our analysis, π 2 ( β ) is considered belonging to the interval [0 , 12 ].”
MethodQuantum metrology with linear Lie algebra parameterizations
Lecamwasam, R., Iakovleva, T., & Twamley, J. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043137 · Cited by 6
“There are also diverse applications beyond sensing, examples include quantum resource theories [8], phase transitions [9–11], entanglement [12, 13], thermodynamics [14], and even quantum error correction [15].”
BackgroundLimits to Velocity of Signal Propagation in Many-Body Systems: A Quantum Information Perspective
Wysocki, P., & Chwedeńczuk, J. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.020201 · Cited by 4
“…usually invoked in the context of quantum metrology, as it sets the lower bound to the sensitivity of quantum sensors [23], the QFI is a versatile tool, allowing to determine the strength of multipar-tite entanglement [24–26], the Einstein-Podolsky-Rosen steering [27], or the Bell nonlocality [28].”
Harnessing quantum chaos in spin-boson models for all-purpose quantum-enhanced sensing
Zhang, Y., Castro, J. C. Z., & Lewis-Swan, R. J. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013227 · Cited by 5
Entanglement in the pseudogap regime of cuprate superconductors
Bippus, F., Krsnik, J., Kitatani, M., Akšamović, L., Kauch, A., Barišić, N., & Held, K. (2025) · Physical review. B./Physical review. B · doi:10.1103/xk42-b9cx · Cited by 4
Quantum Fisher Information of an Open and Noisy System in the Steady State
Altıntaṣ, A. A. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/766/1/012011 · Cited by 5
Observation of photonic states dynamics in 3-D integrated Fourier circuits
Flamini, F., Viggianiello, N., Giordani, T., Bentivegna, M., Spagnolo, N., Crespi, A., Corrielli, G., Osellame, R., Martin-Delgado, M. A., & Sciarrino, F. (2018) · Journal of Optics · doi:10.1088/2040-8986/aac68b · Cited by 4
The effect of nonequilibrium entropy production on the quantum Fisher information and correlations
Wang, X., & Wang, J. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03277-9 · Cited by 5
“Those measurements that can saturate the quantum Cramér-Rao bound are called optimal distinguishing measurements [6, 22, 32].”
BackgroundPrepare non-classical collective spin state by designing control fields
Zhao, X., Ma, Y. L., Ma, H., Qiu, T., & Yi, X. X. (2021) · Physics Letters A · doi:10.1016/j.physleta.2021.127874 · Cited by 4
Quantum Dichotomies and Coherent Thermodynamics beyond First-Order Asymptotics
Lipka-Bartosik, P., Chubb, C. T., Renes, J. M., Tomamichel, M., & Korzekwa, K. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.020335 · Cited by 8
Detection of genuine multipartite entanglement based on principal basis matrix representations
Zhao, H., Liu, Y.-Q., Fei, S.-M., Wang, Z., & Jing, N. (2022) · Laser Physics Letters · doi:10.1088/1612-202x/ac50af · Cited by 4
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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