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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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Desaules, J.-Y., Pietracaprina, F., Papić, Z., Goold, J., & Pappalardi, S. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.020601 · Cited by 56
Multipartite entanglement in the measurement-induced phase transition of the quantum Ising chain
Paviglianiti, A., & Silva, A. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.184302 · Cited by 54
“[45] and [46], this quantity can be used to witness multipartite entanglement when Ô = Ô[{nj}] = 12 ∑ j nj · σ̂j , where nj are unit vectors.”
BackgroundEntanglement and extreme spin squeezing for a fluctuating number of indistinguishable particles
Hyllus, P., Pezzè, L., Smerzi, A., & Tóth, G. (2012) · Physical Review A · doi:10.1103/physreva.86.012337 · Cited by 52
Self-citationQuantum-limited Euler angle measurements using anticoherent states
Goldberg, A. Z., & James, D. F. V. (2018) · Physical Review A · doi:10.1103/physreva.98.032113 · Cited by 54
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
Frérot, I., & Roscilde, T. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.075121 · Cited by 50
Entanglement criterion for multipartite systems based on quantum Fisher information
Akbari-Kourbolagh, Y., & Azhdargalam, M. (2019) · Physical Review A · doi:10.1103/physreva.99.012304 · Cited by 48
Multipartite Entanglement Structure in the Eigenstate Thermalization Hypothesis
Brenes, M., Pappalardi, S., Goold, J., & Silva, A. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.040605 · Cited by 58
Probing quantum correlations in many-body systems: a review of scalable methods
Frérot, I., Fadel, M., & Lewenstein, M. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acf8d7 · Cited by 60
Algebraic many-body localization and its implications on information propagation
Tomasi, G. D. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.054204 · Cited by 51
Sciara, S., Reimer, C., Kues, M., Roztocki, P., Cino, A. C., Moss, D., Caspani, L., Munro, W. J., & Morandotti, R. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.120501 · Cited by 49
Haine, S. A. (2018) · Physical Review A · doi:10.1103/physreva.98.030303 · Cited by 48
Machine-Designed Sensor to Make Optimal Use of Entanglement-Generating Dynamics for Quantum Sensing
Haine, S. A., & Hope, J. J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.060402 · Cited by 48
“Assuming an initial state with no interparticle entanglement (ie, a coherent spin state (CSS) [28]), the maximum possible value is f0 = N , or FQ = NT 2 [17, 18], which we define as the shot-noise limit.”
BackgroundDetection of genuine tripartite entanglement by multiple sequential observers
Maity, A. G., Das, D., Ghosal, A., Roy, A., & Majumdar, A. S. (2020) · Physical Review A · doi:10.1103/physreva.101.042340 · Cited by 46
“[4] P.”
Background
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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