RT Journal Article
SR Electronic
T1 Self-testing nonprojective quantum measurements in prepare-and-measure experiments
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP eaaw6664
DO 10.1126/sciadv.aaw6664
VO 6
IS 16
A1 Tavakoli, Armin
A1 Smania, Massimiliano
A1 Vértesi, Tamás
A1 Brunner, Nicolas
A1 Bourennane, Mohamed
YR 2020
UL http://advances.sciencemag.org/content/6/16/eaaw6664.abstract
AB 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.