Quantum characterization of bipartite Gaussian states

Abstract

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 details 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 provide a reliable reconstruction of the covariance matrix and allows to retrieve all the physical information about the state under investigation. These includes observable quantities, as energy and squeezing, as well as non observable ones as purity, entropy and entanglement. Our procedure also includes advanced tests for Gaussianity of the state and, overall, represents a powerful tool to study bipartite Gaussian state from the generation stage to the detection one

Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering

“…Further, the inequality Ent B|A (ḡ) < 1 for an optimally selectedḡ = g B|A sym that minimises Ent B|A (ḡ) [30] is equivalent to Simon's positive partial transpose condition for entanglement [43], which is necessary and sufficient for two-mode Gaussian states. The parameter defined as Ent ≡ Ent B|A (g symplectic eigenvalue of the partial transpose ν, which determines the logarithmic negativity a measure of entanglement [19,20,29,44]. Maximum entanglement corresponds to Ent → 0.…”

Quantum optics in the phase space

“…Conditional measurements are extremely important in quantum information processing, since they are at the basis of quantum teleportation and telecloning protocols and allow to generate and manipulate new classes of states [75]. Furthermore, a single homodyne detector has been recently used to fully characterize a two-mode squeezed thermal state [76,77].…”

Nonclassical correlations in non-Markovian continuous-variable systems

“…Though there exist separability criteria and entanglement measures for a bipartite Gaussian state (see, e.g., [30][31][32]), in this paper we study the entanglement dynamics by focusing on the logarithmic negativity defined as [33] …”