Hermite-Gaussian model for quantum states
Mathematical Physics
2019-09-04 v1 Information Theory
math.IT
math.MP
Abstract
In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for this model, and we show its relation with the one-dimensional quantum harmonic oscillator. Moreover, using this model we characterize some failies of states of the quantum harmonic oscillator. We find that for the eigenstates of the Hamiltonian, mixtures of eigenstates and even or odd superpositions of eienstates the associated Fisher-Rao metrics are diagonal.
Cite
@article{arxiv.1811.01207,
title = {Hermite-Gaussian model for quantum states},
author = {Marcelo Losada and Ignacio S. Gomez and Federico Holik},
journal= {arXiv preprint arXiv:1811.01207},
year = {2019}
}