Optimality of semiquantum nonlocality in the presence of high inconclusive rates

Quantum nonlocality is a counterintuitive phenomenon that lies beyond the purview of causal influences. Recently, Bell inequalities have been generalized to the case of quantum inputs, leading to a powerful family of semi-quantum Bell inequalities that are capable of detecting any entangled state. Here, we focus on a different problem and investigate how the local-indistinguishability of quantum inputs and postselection may affect the requirements to detect semi-quantum nonlocality. To this end, we consider a semi-quantum nonlocal game based on locally-indistinguishable qubit inputs and derive its postselected local and quantum bounds by using a novel connection to the local-distinguishability of quantum states. Interestingly, we find that the postselected local bound is independent of the measurement efficiency and that the Bell violation increases with lower measurement efficiencies.