Tavakoli Armin, Smania Massimiliano, Vértesi Tamás, Brunner Nicolas, Bourennane Mohamed
Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland.
Department of Physics, Stockholm University, S-10691 Stockholm, Sweden.
Sci Adv. 2020 Apr 17;6(16):eaaw6664. doi: 10.1126/sciadv.aaw6664. eCollection 2020 Apr.
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.
自测试是量子系统认证的最强形式。在此，我们从理论和实验两方面研究非投影量子测量的自测试。也就是说，如何仅从观测数据就证明一个未表征的测量设备实现了所需的非投影正算子值测量（POVM）。我们考虑在希尔伯特空间维度有界的制备 - 测量场景，并开发了用于（i）稳健地自测试极值量子比特POVM和（ii）证明一个未表征的量子比特测量是非投影的方法。我们的方法对噪声具有鲁棒性，因此在实际中适用，正如我们在一个光子实验中所展示的那样。具体而言，我们表明我们的实验数据意味着所实现的测量非常接近某些理想的三结果和四结果量子比特POVM，因此是非投影的。在后一种情况下，数据证明了一个真正的四结果量子比特POVM。我们的结果为量子设备的半设备无关认证开辟了有趣的前景。
