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arXiv · 2601.17662

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

Shan Gao
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Abstract

The Pusey-Barrett-Rudolph (PBR) theorem establishes $\psi$-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 $\psi$-epistemic models for individual systems. In this work, we show that this understanding is incomplete: once the PBR theorem establishes $\psi$-onticity for composite systems prepared in product states, the $\psi$-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 $\psi$-epistemic models, and strengthens the conceptual foundations of $\psi$-ontology.

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Shan Gao. 2026-01-25. From Joint to Single-System Psi-Onticity Without Preparation Independence. https://doi.org/10.1007/s10701-025-00910-w

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