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Pre-entaglement shows that individual quantum systems do not possess states

We consider an experiment in which quantum tomography data is collected before and after an entangling measurement performed on two independently prepared, maximally-mixed ensembles. We show that each sub-ensemble that is, as expected, entangled after the measurement is also entangled before it. We call the latter pre-entanglement. If individual systems possessed quantum states, their independent preparations would mean the sub-ensembles were in separable states prior to the entanglement event. The contradiction can be resolved by assigning states only to ensembles and not individual quantum systems. Pre-entanglement found here at the quantum level makes very doubtful the assumption of preparation independence at the ontic level required for a recent theorem.