Semi-device-independent characterization of quantum measurements under a minimum overlap assumption
Weixu Shi, Yu Ping Cai, Jonatan Bohr Brask, Hugo Zbinden, Nicolas Brunner · Physical Review A · 2019
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 the problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine three-outcome positive-operator valued measures (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.