Understand
We study the extent to which \psi-epistemic models for quantum measurement statistics---models where the quantum state does not have a real, ontic status---can explain the indistinguishability of nonorthogonal quantum states.
- This is done by comparing the overlap of any two quantum states with the overlap of the corresponding classical probability distributions over ontic states in a \psi-epistemic model.
- It is shown that in Hilbert spaces of dimension $d \geq 4$, the ratio between the classical and quantum overlaps in any \psi-epistemic model must be arbitrarily small for certain nonorthogonal states, suggesting that such models are arbitrarily bad at explaining the indistinguishability of quantum states.
- For dimensions $d$ = 3 and 4, we construct explicit states and measurements that can be used experimentally to put stringent bounds on the ratio of classical-to-quantum overlaps in \psi-epistemic models, allowing one in particular to rule out maximally \psi-epistemic models more efficiently than previously proposed.