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Quantum and Fisher information from the Husimi and related distributions
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10.1063/1.2168125
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Affiliations:
1 ISBER, University of California, Santa Barbara, California 93106
a) Electronic mail: slater@kitp.ucsb.edu
J. Math. Phys. 47, 022104 (2006)
/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

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.

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 .

FIG. 3.

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

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 .

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.

FIG. 6.

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

FIG. 7.

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

FIG. 8.

Radial components of and . The latter dominates the former.

FIG. 9.

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

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.

/content/aip/journal/jmp/47/2/10.1063/1.2168125
2006-02-24
2014-04-17

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