Fisher-information susceptibility for multiparameter quantum estimation
Open accessAbstract
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher-information measurement noise susceptibility now allows one to quantify the robustness of measurement for single-parameter estimation. Here we extend this notion to the multiparameter quantum estimation scenario. We provide its mathematical definition in the form of a semidefinite program. Although a closed formula could not be found, we further derive an upper and a lower bound to the susceptibility. We then apply these techniques to two paradigmatic examples of multiparameter estimation: the joint estimation of phase and phase diffusion and the estimation of the different parameters describing the incoherent mixture of optical point sources. Our figure of merit provides clear indications on conditions allowing or hampering robustness of multiparameter measurements.
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The QFI of a density matrix allows determining whether a quantum system is susceptible to perturbations that may affect its quantum coherence.
“The QFI of a density matrix (denoted as QFIM) allows us to determine whether a quantum system is susceptible to perturbations that may affect its quantum coherence [2].”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [2]
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- Authors
- Albarelli, F., Gianani, I., Genoni, M. G., & Barbieri, M.
- Affiliations
- Scuola Normale Superiore (IT)
- Roma Tre University (IT)
- University of Milan (IT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2024-09-26
- Volume
- 110
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W4402861655
- Cited by
- 6
- References
- 64
- Citations by year
- 2026: 3 · 2025: 3
- FWCI
- 0.89
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) (submittedVersion, other-oa)
- Scuola Normale Superiore di Pisa (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Ministero dell'Università e della Ricerca (PRIN22-RISQUE-2022T25TR3)
- H2020 Marie Skłodowska-Curie Actions (101068347)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Fisher information, multiparameter quantum estimation, quantum metrology, semidefinite programming, figure of merit
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