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arXiv · 0805.1645

Quantifying the non-Gaussian character of a quantum state by quantum relative entropy

Marco G. Genoni·Matteo G. A. Paris·Konrad Banaszek
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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.

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Marco G. Genoni, Matteo G. A. Paris, Konrad Banaszek. 2009-01-07. Quantifying the non-Gaussian character of a quantum state by quantum relative entropy. https://doi.org/10.1103/physreva.78.060303

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