Entanglement, one of the most intriguing aspects of quantum mechanics, marks itself into different features of quantum states. For this reason different criteria can be used for verifying entanglement. In this paper we review some of the entanglement
criteria casted for continuous variable states and link them to peculiar aspects of the original debate on the famous EPR paradox. Moreover, we give a handy expression for valuating Bell-type non-locality on Gaussian states. We also present the experimental measurement of a particular realization of the Bell operator over continuous variable entangled states produced by a sub-threshold type-II OPO.
We propose a quantum optics experiment where a single two-mode Gaussian entangled state is used for realizing the paradigm of an amendable Gaussian channel recently presented in Phys. Rev. A, textbf{87}, 062307 (2013). Depending on the choice of the
experimental parameters the entanglement of the probe state is preserved or not and the relative map belongs or not to the class of entanglement breaking channels. The scheme has been optimized to be as simple as possible: it requires only a single active non-linear operation followed by four passive beam-splitters. The effects of losses, detection inefficiencies and statistical errors are also taken into account, proving the feasibility of the experiment with current realistic resources.
Quantum properties are soon subject to decoherence once the quantum system interacts with the classical environment. In this paper we experimentally test how propagation losses, in a Gaussian channel, affect the bi-partite Gaussian entangled state ge
nerated by a sub-threshold type-II optical parametric oscillator (OPO). Experimental results are discussed in terms of different quantum markers, as teleportation fidelity, quantum discord and mutual information, and continuous variables (CV) entanglement criteria. To analyse state properties we have retrieved the composite system covariance matrix by a single homodyne detector. We experimentally found that, even in presence of a strong decoherence, the generated state never disentangles and keeps breaking the quantum limit for the discord. This result proves that the class of CV entangled states discussed in this paper would allow, in principle, to realize quantum teleportation over an infinitely long Gaussian channel.
We experimentally verify uncertainty relations for mixed states in the tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of single-mode radiation field are discussed in details as parad
igm of mixed quantum state. By considering the connection between generalised uncertainty relations and optical tomograms is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critically on the purity of the information carrier states. In this contest the homodyne detector becomes an easy to handle purity-meter for the state on-line with a running quantum information protocol.
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 de
tails 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.
