On Fisher Information of Quantum Statistical Models

2005 ◽  
pp. 113-124 ◽  
Author(s):  
Hiroshi Nagaoka
Keyword(s):  
Fisher Information ◽  
Statistical Models ◽  
Quantum Statistical

scholarly journals Taming singularities of the quantum Fisher information

2021 ◽  
Author(s):  
Aaron Z. Goldberg ◽  
José L. Romero ◽  
Ángel S. Sanz ◽  
Luis L. Sánchez-Soto
Keyword(s):  
Density Matrix ◽  
Fisher Information ◽  
Statistical Models ◽  
Probability Distributions ◽  
Quantum Fisher Information ◽  
Quantum Metrology ◽  
Quantum Statistical ◽  
Information Matrices ◽  
Parameter Dependent ◽  
Ultimate Limit

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.

About the quantum Fisher information of nearly pure quantum statistical models

2020 ◽  
Vol 18 (01) ◽  
pp. 1941022
Author(s):  
Matteo G. A. Paris
Keyword(s):  
Fisher Information ◽  
Statistical Models ◽  
Logarithmic Derivative ◽  
Quantum Fisher Information ◽  
Independent State ◽  
Approximate Analytic Expression ◽  
Weak Source ◽  
Pure States ◽  
Analytic Expression ◽  
Quantum Statistical

We address nearly pure quantum statistical models, i.e. situations where the information about a parameter is encoded in pure states weakly perturbed by the mixing with a parameter independent state, mimicking a weak source of noise. We show that the symmetric logarithmic derivative is left unchanged, and find an approximate analytic expression for the quantum Fisher information (QFI) which provides bounds on how much a weak source of noise may degrade the QFI.

Capturing H and H2by SiHx+(x≤ 4) ions: Comparison between Langevin and quantum statistical models

2017 ◽  
Vol 56 (2) ◽  
pp. 026101 ◽  
Author(s):  
Trong-Nghia Nguyen ◽  
Yun-Min Lee ◽  
Jong-Shinn Wu ◽  
Ming-Chang Lin
Keyword(s):  
Statistical Models ◽  
Quantum Statistical

Quantum-statistical models for multicomponent plasmas

1976 ◽  
Vol 14 (6) ◽  
pp. 2295-2300 ◽  
Author(s):  
Balazs F. Rozsnyai ◽  
Berni J. Alder
Keyword(s):  
Statistical Models ◽  
Quantum Statistical

scholarly journals Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 703 ◽  
Author(s):  
Jun Suzuki
Keyword(s):  
Statistical Model ◽  
Error Bound ◽  
Statistical Models ◽  
Estimation Error ◽  
Estimation Theory ◽  
Geometrical Characterization ◽  
Classical Models ◽  
Quantum Statistical ◽  
Equivalent Conditions

In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model.

scholarly journals Asymptotic inference in system identification for the atom maser

2012 ◽  
Vol 370 (1979) ◽  
pp. 5308-5323 ◽  
Author(s):  
Cătălin Cătană ◽  
Merlijn van Horssen ◽  
Mădălin Guţă
Keyword(s):  
System Identification ◽  
Fisher Information ◽  
Statistical Models ◽  
Quantum Fisher Information ◽  
Asymptotic Statistics ◽  
Quantum Dynamical ◽  
Process Tomography ◽  
Quantum Markov Processes ◽  
Set Up ◽  
Quantum Dynamical Systems

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

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