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The chained Bell inequalities of Braunstein and Caves involving N settingsper observer have some interesting applications. Here we obtain the minimumdetection efficiency required for a loophole-free violation of theBraunstein-Caves inequalities for any N > 2. We discuss both the case in whichboth particles are detected with the same efficiency and the case in which theparticles are detected with different efficiencies.

Minimum detection efficiency for a loophole-free violation of the Braunstein-Caves chained Bell inequalities