Two definitions of maximally ψ-epistemic ontological model and preparation non-contextuality

Abstract An ontological model is termed as maximally ψ -epistemic if the overlap between any two quantum states fully accounted for by of their respective probability distributions ontic states. However, in literature, there exist different mathematical definitions (termed here 1M E and 2M E) that capture equivalent notion maximal -epistemicity. In this work, we provide three theorems to critically examine connections preparation non-contextuality aforementioned theorem 1, a simple direct argument an existing proof demonstrate mixed state implies first definition 2, prove second -epistemicity pure-state non-contextuality. If both -epistemicity, then from one infers mixed-state But, 3, contextuality vice versa. This leads conclude inequivalent notions The implications our results other no-go are discussed.