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

Optimality of semiquantum nonlocality in the presence of high inconclusive rates