Tomography of spin states, the entanglement criterion, and Bell's inequalities

We review the method of spin tomography or quantum states in which we use the standard probability distribution functions to describe spin projections oil selected directions, which provides the same information about states as is obtained by the density matrix method. In this approach, we show that satisfaction or violation of Bell's inequalities can be understood as properties of tomographic functions for joint probability distributions for two spins. We compare results obtained using the methods or classical probability theory with those obtained in the framework or traditional quantum mechanics.