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In this paper, we investigate a characterization of Quantum Mechanics by twophysical principles based on general probabilistic theories. We first give theoperationally motivated definition of the physical equivalence of states andconsider the principle of the physical equivalence of pure states, which turnsout to be equivalent to the symmetric structure of the state space. We furtherconsider another principle of the decomposability with distinguishable purestates. 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.

Physical Equivalence of Pure States and Derivation of Qubit in General Probabilistic Theories