arXiv:0704.0639 · Physical Review A

Measure of the non-Gaussian character of a quantum state

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

Published Oct 22, 2007• 169 citations

Abstract

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in detail the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single-mode and multimode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows one to define a corresponding measure for the non-Gaussian character of a quantum operation.

DOI: 10.1103/physreva.76.042327

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