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arXiv · 0704.0639

A measure of the non-Gaussian character of a quantum state

Marco G. Genoni·Matteo G. A. Paris·Konrad Banaszek
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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 details the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single- and multi-mode 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 to define a corresponding measure for the non-Gaussian character of a quantum operation.

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Marco G. Genoni, Matteo G. A. Paris, Konrad Banaszek. 2007-10-02. A measure of the non-Gaussian character of a quantum state. https://doi.org/10.1103/physreva.76.042327

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