From Joint to Single-System Psi-Onticity Without Preparation Independence

The Pusey-Barrett-Rudolph (PBR) theorem establishes ψ-onticity for individual quantum systems, but its standard formulation relies on the Preparation Independence Postulate (PIP). This has led to a prevalent view that rejecting PIP leaves open the possibility of ψ-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes ψ-onticity for composite systems prepared in product states, the ψ-onticity of the individual subsystems follows directly from the tensor-product structure of quantum mechanics, without invoking PIP or any further auxiliary assumptions. This result removes a key auxiliary assumption from the PBR theorem, closes a persistent loophole for preserving ψ-epistemic models, and strengthens the conceptual foundations of ψ-ontology.