A higher quantum bound for the V\'ertesi-Bene-Bell-inequality and the role of POVMs regarding its threshold detection efficiency

摘要: Recently, V\'{e}rtesi and Bene [Phys. Rev. A. {\bf 82}, 062115 (2010)] derived a two-qubit Bell inequality, $I_{CH3}$, 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. Here we consider parametrization for three-element-POVM involved in test obtain higher quantum bound $I_{CH3}$-inequality. With investigate if there is an experimental setup that can observing POVMs give violations tests based on this inequality. We analyze maximum errors supported by inequality identify source entangled photons test. Then, study also relevant realistic case partially states experiment. Finally, required efficiencies $I_{CH3}$-inequality, type measurements involved, closing detection loophole. allow lowest threshold efficiency, it comparable minimal (in two-qubits) efficiency Clauser-Horne-Bell-inequality.