Minimal classical pure-state model conjecture

Let a generic physical statistical system have a set of pure states, and let a classical physical system reproduce its statistical phenomenology. A pure-state correspondence is a one-to-one correspondence between the pure states of the two systems.

Minimal classical pure-state model conjecture. The simplest classical physical system capable of reproducing the statistical phenomenology of a generic physical statistical system, such as a quantum one, is one whose pure states are in one-to-one correspondence with the pure states of the generic system. In the quantum case, models such as the Beltrametti–Bugajski model, using Holevo's construction, are the simplest possible.

The claim translates the preceding convex-geometric refinement questions into a physical requirement on classical models reproducing quantum phenomenology. The source supplies no proof or disproof in the excerpt and presents it as a conjecture.