New hidden variable theory of a two-dimensional quantum system

There exist some no-go theorems which say that it is impossible to construct realistic theory for quantum systems without contradictions. We, however, proposed in a recent paper a method to escape the so-called Bell-style paradox. Reasonable further research would be to embody our proposition in a concrete hidden-variable theory. As preliminary study, we try to extract lessons from a two-dimensional case. Although it is well known that a two-dimensional hidden-variable theory can be constructed without inconsistency with a quantum formalism, our model given here differs from the old ones in that ours has a possibility of being generalized to a higher dimensional system. Moreover, it is equipped with a non-uniform measure which is determined by the choice of a state.