  In this paper, we investigate a characterization of Quantum Mechanics by two
physical principles based on general probabilistic theories. We first give the
operationally motivated definition of the physical equivalence of states and
consider the principle of the physical equivalence of pure states, which turns
out to be equivalent to the symmetric structure of the state space. We further
consider another principle of the decomposability with distinguishable pure
states. We give classification theorems of the state spaces for each principle,
and derive the Bloch ball in 2 and 3 dimensional systems by these principles.
