Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography

摘要

We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure ofHorodecki et al. [Phys. Lett.A200, 340 (1995)] and the fully entangled fraction of Bennett et al. [Phys. Rev.A54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.