Measurement ordering contextuality and the search for psi-epistemic theories

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We prove that all non-conspiratorial/retro-causal hidden variable theories has to be measurement ordering contextual, i.e. there exists
*commuting* operator pair (A,B) and a hidden state \\\\lambda such that the outcome of A depends on whether we measure B before or after.
Interestingly this rules out a recent proposal for a psi-epistemic due to Barrett, Hardy, and Spekkens. We also show that the model was in fact partly discovered already by vanFraassen 1973; the only thing missing was giving a probability distribution on the space of ontic states (the hidden variables).