Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
arXiv:0805.1645 · doi:10.1103/PhysRevA.78.060303
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.
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
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