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It is well-known that in certain scenarios weakly entangled states cangenerate stronger nonlocal effects than their maximally entangled counterparts.In this paper, we consider violations of the CHSH Inequality when one party hasinefficient detectors, a scenario known as an asymmetric Bell experiment. %Weshow that violations can occur if and only if the detection efficiency is above$50\%$. For any fixed detection efficiency, we derive a simple upper bound onthe entanglement needed to violate the inequality by more than some specifiedamount $\kappa\geq 0$. When $\kappa=0$, the amount of entanglement in allstates violating the inequality goes to zero as the detection efficiencyapproaches $50\%$ from above. %This provides another scenario in which weaklyentangled states are advantageous for violating the CHSH Inequality in thepresence of detection inefficiency. We finally consider the scenario in whichdetection inefficiency arises for only one choice of local measurement. In thiscase, it is shown that the CHSH Inequality can always be violated for anynonzero detection efficiency and any choice of non-commuting measurements.

More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors