A $\psi$-Ontology Result without the Cartesian Product Assumption

TL;DR

This paper weakens a key assumption in quantum foundations to show that certain pairs of quantum states must be ontologically distinct, advancing our understanding of quantum state reality without relying on the Cartesian product assumption.

Contribution

It introduces a new assumption that relaxes the Preparation Independence Postulate, leading to a novel ontological distinction result for quantum states.

Findings

Pairs of pure states with overlap ≤ 1/√2 are ontologically distinct.

The result holds without assuming the Cartesian product structure of subsystem states.

Supports a ψ-ontology result under weaker assumptions.

Abstract

We introduce a weakening of the Preparation Independence Postulate of Pusey, Barrett, and Rudolph that does not presuppose that the space of ontic states resulting from a product state preparation can be represented by the Cartesian product of subsystem state spaces. On the basis of this weakened assumption, it is shown that, in any model that reproduces the quantum probabilities, any pair of pure quantum states $\ket{\psi}$, $\ket{\phi}$ with $\bkt{\phi}{\psi} \leq 1/\sqrt{2}$ must be ontologically distinct.