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Cited by 1,632Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

Quantum estimation for quantum technology

PARIS, MATTEO G. A.·2009·International Journal of Quantum Information
DOI 10.1142/s0219749909004839
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Abstract

Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.

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  • For an unbiased measurement strategy, the variance of the estimate of an unknown parameter is bounded below by the inverse of the number of repetitions times the quantum Fisher information.

    “Under the assumption that our strategy is unbiased, i.e. μ = µ, the uncertainty in our estimate, is related to the variance of μ and is lower bounded by the so-called quantum Cramer-Rao bound”

    From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [100]

  • Dephasing and amplitude damping are naturally occurring sources of decoherence in NMR implementation, and the results can be accessed by spin ensemble measurements.

    “In fact, dephasing and amplitude damping are naturally occurring sources of decoherence in such an implementation, and our results can be accessed by means of spin ensemble measurements, which constitute the conventional types of detection in such a technique [71,72].”

    From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [72]

  • The quantum Cramér-Rao bound sets the ultimate precision for estimating parameters encoded in quantum states.

    “This bound determines the ultimate precision with which parameters encoded into quantum states can be estimated.”

    From Estimation of Gaussian quantum states (2019) · cites this paper as [1]

  • The quantum Fisher information matrix gives the ultimate precision bound on the estimation of parameters encoded in a quantum state.

    “Quantum Fisher information matrix (QFIM) gives the ultimate precision bound on the estimation of parameters encoded in a quantum state.”

    From Simple expression for the quantum Fisher information matrix (2018) · cites this paper as [5]

  • The most general analytical expression for the QFIM requires diagonalizing the density matrix.

    “Still, known expressions for the QFIM appear quite complicated, and the most general analytical expression requires diagonalizing the density matrix.”

    From Simple expression for the quantum Fisher information matrix (2018) · cites this paper as [5]

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Authors
PARIS, M. G. A.
Affiliations
Institute for Scientific Interchange (IT)
Corresponding author
PARIS, MATTEO G. A.
ORCID
PARIS, MATTEO G. A.
Venue
International Journal of Quantum Information
Publisher
World Scientific Pub Co Pte Ltd
Published
2009-01
Volume
07
Issue
supp01
Pages
125-137
ISSN
  • 0219-7499 (ISSN-L)
  • 1793-6918
DOI
10.1142/s0219749909004839
OpenAlex
W1993122650
Cited by
1,632
References
32
Citations by year
2026: 186 · 2025: 204 · 2024: 151 · 2023: 150 · 2022: 146 · 2021: 135 · 2020: 152 · 2019: 118 · 2018: 85 · 2017: 89 · 2016: 70 · 2015: 45 · 2014: 37 · 2013: 16 · 2012: 18
FWCI
16.92
Type
journal article
Language
en
Open access
closed
Locations
International Journal of Quantum Information (publishedVersion)
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
quantum parameter estimation, quantum Fisher information, symmetric logarithmic derivative, entanglement, purity, quantum statistical model, quantum noise, parameter estimation

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