  Stochastic and bistochastic matrices providing positive maps for spin states
(for qudits) are shown to form semigroups with dense intersection with the Lie
groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density
matrix of a qudit state is shown to be described by a spin tomogram determined
by an orbit of the bistochastic semigroup acting on a simplex. A class of
positive maps acting transitively on quantum states is introduced by relating
stochastic and quantum stochastic maps in the tomographic setting. Finally, the
entangled states of two qubits and Bell inequalities are given in the framework
of the tomographic probability representation using the stochastic semigroup
properties.
