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Cited by 70Quantum Mechanics and ApplicationsQuantum Information and CryptographyQuantum Computing Algorithms and Architecture

Geometry of Quantum Statistical Inference

Brody, Dorje C., Hughston, Lane P.·1996·Physical Review Letters
DOI 10.1103/physrevlett.77.2851
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Abstract

An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry. This theory, which allows for a transparent transition between classical and quantum statistical inference, is then applied to the analysis of exponential families of distributions (of relevance to statistical mechanics) and quantum mechanical evolutions. The extension to quantum theory is achieved by the introduction of a complex structure on the given real Hilbert space. We find a set of higher order corrections to the parameter estimation variance lower bound, which are potentially important in quantum mechanics, where these corrections appear as modifications to Heisenberg uncertainty relations for the determination of the parameter.

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  • The analytical formulas of the fidelity F(ρ0,ρτ) and the affinity A(ρ0,ρτ) for any pair of one-qubit states are given by Eqs. (A12) and (A13).

    “where the analytical formulas of the fidelity Fðρ 0 ; ρ τ Þ and the affinity Aðρ 0 ; ρ τ Þ for any pair of one-qubit states ρ 0 and ρ τ are the following [29,73,74]:”

    From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [73]

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Research works printed but not linked: 1

  1. [7]L. P. Hughston, in Twistor Theory, edited by S. Huggett ( Marcel Dekker, Inc., New York, 1995); Proc. R. Soc. London 452 , 953 (1996); J. Anandan and Y. Aharonov, Phys. Rev. Lett. 65 , 1697 (1990); A. Ashtekar and T. A. Schilling, in CAM-94 Physics Meeting, edited by A. Zepeda, AIP Conf. Proc. No. 342 (AIP Press, Woodbury, NY, 1995).

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Authors
Brody, D. C., & Hughston, L. P.
Affiliations
Imperial College London (GB)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1996-09-30
Volume
77
Issue
14
Pages
2851-2854
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.77.2851
OpenAlex
W1977587840
Cited by
70
References
9
Citations by year
2026: 1 · 2025: 5 · 2024: 3 · 2022: 4 · 2021: 3 · 2020: 4 · 2019: 3 · 2018: 4 · 2017: 2 · 2016: 1 · 2013: 4 · 2012: 5
FWCI
2.64
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • Goldsmiths (University of London) (acceptedVersion)
  • UCL Discovery (University College London) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
quantum statistical inference, parameter estimation, Hilbert space geometry, exponential family, complex structure, Cramer-Rao lower bound, higher-order corrections, uncertainty principle, quantum-to-classical transition

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