J. F. Barra, E. S. Gómez, G. Cañas, W. A. T. Nogueira, L. Neves, G. Lima
Recently, V\'ertesi and Bene [Phys. Rev. A. 82, 062115 (2010)] derived a two-qubit Bell inequality, ICH3, which they show to be maximally violated only when more general positive operator valued measures (POVMs) are used instead of the usual von Neumann measurements. For the case of a maximally entangled state (MES) they give, explicitly, the elements of a POVM which outperforms the maximum allowed for ICH3 with projective measurements. Here, we consider a general parametrization for the three-element-POVM involved in the test, and study further properties of the ICH3-inequality. First, we restrict ourselves to the MES case and obtain a higher quantum bound for the ICH3-inequality with POVMs. Our goal is to study whether it is possible or not to observe the relevance of POVMs in a Bell test based on this inequality, when typical experimental errors are taken into account. Then, we study if POVMs are also relevant in the more realistic case that partially entangled states are used in the test. Finally, we investigate which are the required efficiencies of the ICH3-inequality, and the type of measurements involved, for closing the detection loophole. Surprisingly, we obtain that a rank-2 POVM allows for the lowest threshold detection efficiency, which is comparable to the minimal (in the case of two-qubits) required detection efficiency of the Clauser-Horne-Bell-inequality.
View original:
http://arxiv.org/abs/1207.0712
No comments:
Post a Comment