Operational reconstruction of quantum single-system state spaces

Derive a set of operational conditions sufficient to identify the quantum state space for single systems, thereby complementing the mutual-superposition characterization of the quantum tensor-product composition rule.

Background

The main result characterizes the quantum tensor product as the largest composition of quantum systems that admits mutual superposition under the stated assumptions. However, that result presupposes that the component systems already have quantum state spaces. The paper therefore leaves unresolved the single-system reconstruction problem: finding operational principles that select quantum state spaces themselves.