Entanglement quantification through local observable correlations

We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we demonstrate that it's possible to define a measure which is invariant under local unitary transformations and which is based only on local measurements. It is quite simple to implement experimentally and it allows entanglement quantification in a certain range for mixed states and exactly for pure states, without first obtaining full knowledge (e.g. through tomography) of the state.Comment: 5 pages, 3 figures, revised version with new proof and replaced figure

Central-moment description of polarization for quantum states of light

We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincar\'{e} sphere, and provide a method of polarization tomography without resorting to full state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.Comment: 11 pages, 7 figures, 4 tables, In version 2, Figs. 2 and 4 are replaced, Sec. IV extended, Sec. VIII revised, a few references adde

Experimental entanglement verification and quantification via uncertainty relations

We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by which entanglement quantification is implemented for two-qubit pure states. The nonlocal uncertainty relations for two-qubit pure states are also used for entanglement verification which serves as a basic proposition and promise to be a good choice for verification of multipartite entanglement.Comment: 5 pages, 3 figures and 2 table