Sufficient condition for a quantum state to be genuinely quantum non-Gaussian
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2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. We showthat the expectation value of the operator O exp(-cx2) + exp(-cp2) defined by the position and momentum operators x and p with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures.We demonstrate that our method is even able to detect quantum non-Gaussian states with positive- definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phasespace distribution. Moreover, we demonstrate that our condition can characterize quantum non- Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50%signal attenuation.