The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED is a faithful measure of incompatibility for sharp observables and provides a metric on the space of von Neumann measurements. It can be efficiently estimated by letting the measurements act in an indefinite order, using a setup known as the quantum switch. Thanks to these features, the MED can be used in quantum machine learning tasks, such as clustering quantum measurement devices based on their mutual compatibility. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise can be used to identify groups of observers that share approximately the same measurement context.

翻译：不相容的可观测物的存在是量子力学的基石,也是量子技术的宝贵资源。在这里,我们引入了一种不相容的量子力学,称为相互的天体扰动(MED),它量化了测量在另一个人脑空间的锐视性所引发的扰动量。MED是精确地测量锐视的不相容性的一种尺度,为冯纽曼测量空间提供了一种度量度尺度。它可以通过使用量子开关的设置无限期地让测量活动进行有效估算。由于这些特征,MED可用于量子机学习任务,例如基于相互兼容性的组合量量测量装置。我们通过提供一种不为人知的算法,即冯纽曼测量数据组,来证明这种应用。我们的算法对于噪音是强大的,可以用来识别与测量环境大致相同的观察者群体。