  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.
