Detecting Quantum States with a Positive Wigner Function beyond Mixtures of Gaussian States

Abstract

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime. DOI: http://dx.doi.org/10.1103/PhysRevLett.106.200401 © 2011 American Physical Society