Quantum characterization of bipartite Gaussian states

Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in detail and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled cw frequency degenerate beams. The method provides a reliable reconstruction of the covariance matrix and allows us to retrieve all the physical information about the state under investigation. These include observable quantities, such as energy and squeezing, as well as nonobservable ones such as purity, entropy, and entanglement. Our procedure also includes advanced tests for the Gaussianity of the state and, overall, represents a powerful tool to study the bipartite Gaussian state from the generation stage to the detection one.