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

Abstract: 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.