Higher quantum bound for the V´ertesi-Bene-Bell inequality and the role of positive operator-valued measures regarding its threshold detection efficiency

摘要

Recently, V′ertesi and Bene [Phys. Rev. A 82, 062115 (2010)] derived a two-qubit Bell inequality ICH3, whichnthey show to be maximally violated only when more general positive operator-valued measures (POVMs) arenused instead of the usual von Neumann measurements. Here we consider a general parametrization for thenthree-element POVM involved in the Bell test and obtain a higher quantum bound for the ICH3 inequality. Withna higher quantum bound for ICH3, we investigate whether there is an experimental setup that can be used fornobserving that POVMs give higher violations in Bell tests based on this inequality. We analyze the maximumnerrors supported by the inequality to identify a source of entangled photons that can be used for the test. Then wenstudy whether POVMs are also relevant in the more realistic case where partially entangled states are used in thenexperiment. Finally, we investigate the required efficiencies of the ICH3 inequality, and the type of measurementsninvolved, for closing the detection loophole. We obtain the result that POVMs allow for the lowest thresholdndetection efficiency, and that it is comparable to the minimal required detection efficiency (in the case of twonqubits) of the Clauser-Horne-Bell inequality.