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Fisher information and multiparticle entanglement

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Hyllus, Philipp, Laskowski, Wiesław, Krischek, Roland, Schwemmer, Christian, Wieczorek, Witlef, Weinfurter, Harald, Pezzé, Luca, Smerzi, Augusto·2012·Physical Review A

DOI 10.1103/physreva.85.022321

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Abstract

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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Finite-resolution entanglement depth of W states: exact trace distance to the mixed k-producible hierarchy
Sun, W., Shao, X., & Jin, Y. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05353-4

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)
ORCID: Laskowski, Wiesław
Schwemmer, Christian
Wieczorek, Witlef
Weinfurter, Harald
Smerzi, Augusto
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
DOI: 10.1103/physreva.85.022321
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
Licence: link.aps.org/licenses/aps-default-license (vor)
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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Fisher information and multiparticle entanglement

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