Recently, a novel framework for semi-device-independent quantum
prepare-and-measure protocols has been proposed, based on the assumption of a
limited distinguishability between the prepared quantum states. Here, we
discuss the problem of characterizing an unknown quantum measurement device in
this setting. We present several methods to attack this problem. Considering
the simplest scenario of two preparations with lower bounded overlap, we show
that genuine 3-outcome POVMs can be certified, even in the presence of noise.
Moreover, we show that the optimal POVM for performing unambiguous state
discrimination can be self-tested.Comment: 9 pages,7 figure
