%0 Journal Article
%A Tavakoli, Armin
%A Smania, Massimiliano
%A Vértesi, Tamás
%A Brunner, Nicolas
%A Bourennane, Mohamed
%T Self-testing nonprojective quantum measurements in prepare-and-measure experiments
%D 2020
%R 10.1126/sciadv.aaw6664
%J Science Advances
%P eaaw6664
%V 6
%N 16
%X Self-testing represents the strongest form of certification of a quantum system. Here, we theoretically and experimentally investigate self-testing of nonprojective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension and develop methods for (i) robustly self-testing extremal qubit POVMs and (ii) certifying that an uncharacterized qubit measurement is nonprojective. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data imply that the implemented measurements are very close to certain ideal three- and four-outcome qubit POVMs and hence non-projective. In the latter case, the data certify a genuine four-outcome qubit POVM. Our results open interesting perspective for semi–device-independent certification of quantum devices.
%U https://advances.sciencemag.org/content/advances/6/16/eaaw6664.full.pdf