Abstract We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons’ polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.

中文翻译：

---

实验确定两个量子位测量的不相容性

摘要我们描述并实现了一种用于评估两个量子位测量不相容性的实验程序。该实验包括状态辨别任务，其中根据一些部分中间信息使用任一测量。该任务的成功统计数据为两个测量的不兼容量提供了上限，因为它是通过它们的不兼容稳健性来量化的。对于一类广泛的无偏和可能有噪声的量子比特测量，可以通过适当调整实验的准备来使这个上限与鲁棒性的真实值一致。我们在光学装置中证明了这一事实，其中量子位状态被编码为光子的偏振自由度，通过对测量的最终投影阶段的幅度、相位和纯度进行精确控制，直接访问不兼容性。因此，我们的工作确立了最近提出的用于检测量子不相容性的方法的实际可行性。