Using Bochner's theorem, we derive a necessary and sufficient hierarchy of measurable conditions in terms of the characteristic function of quasi-moments of a weakly measured observable. A quantum system that violates any of these conditions is nonclassical in weak measurements. Then, we formulate nonclassicality conditions obtained in terms of modular values that can be easily measured by performing a tomography of the final state of a qubit device. This method provides us direct access to the characteristic function as the generating function of quasi moments of weakly measured observable. In this way, We solve the problem of experimental restrictions on measuring the infinite number of weak quasi-moments.

使用Bochner定理，我们根据可测量的弱观测量的准矩的特征函数，得出了可测量条件的必要和充分层次。在弱测量中，违反任何一种条件的量子系统都是非经典的。然后，我们根据模块值制定获得的非经典条件，可以通过对qubit器件的最终状态进行断层扫描轻松地对其进行测量。这种方法使我们可以直接访问特征函数，作为可测量的弱测准矩的生成函数。这样，我们解决了在测量无限数量的弱准矩时的实验限制问题。