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

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.

revised and enlarged version, 7 pages, 4 figures

References in corpus (4)

• Multiphoton Quantum Optics and Quantum State Engineering
• Quantum Capacities of Bosonic Channels
• The optimal cloning of quantum coherent states is non-Gaussian
• De-Gaussification by inconclusive photon subtraction

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