Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
Abstract
We introduce a novel measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in details the properties of our measure and illustrate its relationships with relevant quantities in quantum information as the Holevo bound and the conditional entropy; in particular a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity (nonG) is analyzedfor quantum states undergoing conditional Gaussification towards twin-beam and de-Gaussification driven by Kerr interaction. Our analysis allows to assess nonG as a resource for quantum information and, in turn, to evaluate the performances of Gaussification and de-Gaussification protocols.
Cite
@article{arxiv.0805.1645,
title = {Quantifying the non-Gaussian character of a quantum state by quantum relative entropy},
author = {Marco G. Genoni and Matteo G. A. Paris and Konrad Banaszek},
journal= {arXiv preprint arXiv:0805.1645},
year = {2009}
}
Comments
4 pages, 2 figures. v2: Slightly revised version and reference added. v3: minor corrections, to appear on Phys. Rev. A (Rapid Communication). v4: published version