Nonclassicality of Dirac-Pauli quantum states

In classical physics, a joint measurement of two compatible observables on an enlarged system-apparatus state usually implies that the joint statistics of the corresponding specific system observables are always separable. In this paper, we show that, for the quantum states with its density operators composed of the Dirac-Pauli matrices, the joint statistics of these specific system observables are entangled and the data inversion of the joint statistical distribution is negative. This nonclassical property, which can be revealed by an experimental scheme based on the homodyne detection, maybe helps us to understand the nonlocal features of the quantum tests of the Bell type. When we consider these Dirac-Pauli states as bipartite ones, these bipartite states have a nonzero quantum discord although they are separable.