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Quantum and Fisher information from the Husimi and related distributions
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10.1063/1.2168125
/content/aip/journal/jmp/47/2/10.1063/1.2168125
http://aip.metastore.ingenta.com/content/aip/journal/jmp/47/2/10.1063/1.2168125
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The monotone function that yields the tangential component of the Fisher information metric over the trivariate Husimi probability distributions for the two-level quantum systems.

Image of FIG. 2.
FIG. 2.

The radial components of any monotone metric and that of the Fisher information metric derived from the family of trivariate Husimi distributions over the TLQS. The one for the (nondenumerably infinite) class dominates that for .

Image of FIG. 3.
FIG. 3.

Monotonically decreasing function obtained by equating the volume element of to that of a generic monotone metric (1).

Image of FIG. 4.
FIG. 4.

Plots of one-dimensional marginal probability distributions over the radial coordinate of , , , , and . The order of dominance of the curves is . The marginal distributions of and are quite close, as reflected in their small relative entropy .

Image of FIG. 5.
FIG. 5.

The monotone functions , that yield the tangential components of the Fisher information metric over the escort-Husimi probability distributions. The steepness of the graphs decreases as increases.

Image of FIG. 6.
FIG. 6.

Approximation to the presumed operator monotone function yielding the tangential component of for the positive representation over the two-level quantum systems.

Image of FIG. 7.
FIG. 7.

Approximation to the radial component of for the positive -representation over the two-level quantum systems.

Image of FIG. 8.
FIG. 8.

Radial components of and . The latter dominates the former.

Image of FIG. 9.
FIG. 9.

Scalar curvature of the Fisher information metric for the family of Husimi distributions.

Image of FIG. 10.
FIG. 10.

Statistical distance as a function of distance from the origin of the Bloch ball—corresponding to the fully mixed state—for any monotone metric, for , and for the Monge (or equivalently, for , Hilbert-Schmidt) metric. The monotone-metric curve dominates that for , which dominates the linear curve for the Monge metric.

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/content/aip/journal/jmp/47/2/10.1063/1.2168125
2006-02-24
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum and Fisher information from the Husimi and related distributions
http://aip.metastore.ingenta.com/content/aip/journal/jmp/47/2/10.1063/1.2168125
10.1063/1.2168125
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