PBR theorem and sub-ensemble of quantum state


Abstract
Pusey-Barrett-Rudolph theorem claims that $\psi$-epistemic understanding of quantum mechanics is in trouble. Not considering whether the theorem only applies for realist understanding of quantum theory, this paper instead shows that the actual issue the theorem exposes is whether every quantum state should be interpreted as representing all sub-ensemble possibilities. For example, if $|+\rangle$ was ``measured'' at time $t=0$ where $|+\rangle = /\sqrt{2}$, should we consider this quantum state as being solely $|+\rangle$, or representing all possible sub-ensembles such as $, $? This question suggests that PBR theorem does not rule out realist/non-realist $\psi$-epistemic theory.
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