Two pure qubit states and one mixed state suffice to prove that maximally psi-epistemic ontological models cannot explain a three-outcome guessing game called Quantum Gambling.
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A novel no-go theorem is presented which sets a bound upon the extent to which '\Psi-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance of an underlying state of reality. The theorem applies to any Hilbert space of dimension greater than two. In the limit of large Hilbert spaces, no more than half of the overlap between quantum states can be accounted for. Unlike other recent no-go theorems no additional assumptions, such as forms of locality, invasiveness, or non-contextuality, are required.
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Maximally $\psi-$epistemic models cannot explain gambling with two qubits
Two pure qubit states and one mixed state suffice to prove that maximally psi-epistemic ontological models cannot explain a three-outcome guessing game called Quantum Gambling.