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

TL;DR

This paper explores foundational principles in general probabilistic theories to characterize quantum mechanics, deriving the qubit structure and Bloch ball through physical equivalence and decomposability of pure states.

Contribution

It introduces principles based on physical equivalence and decomposability, providing classification theorems and deriving the qubit structure within a general probabilistic framework.

Findings

Derived the Bloch ball in 2 and 3 dimensions from these principles.

Classified state spaces based on physical equivalence and decomposability.

Established equivalence between certain principles and symmetric state space structures.

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.