Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

L. Happ, M. A. Efremov, Hyunchul Nha, W. P. Schleich

Research output: Contribution to journalArticle

11 Citations (Scopus)


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.

Original languageEnglish
Article number023046
JournalNew Journal of Physics
Issue number2
Publication statusPublished - 1 Feb 2018



  • continuous variables
  • Gaussian state
  • non-Gaussian states
  • quadrature measurements
  • quantum information
  • Wigner functions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this