Epistemic interpretations of quantum theory have a measurement problem

Joshua B. Ruebeck, Piers Lillystone, Joseph Emerson

Published 2018-12-19Version 1

Epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to evade the physicality of the "collapse" process and provide a reasonable account of state update under measurement by asserting that it is a natural feature of simply updating incomplete statistical information. Here we demonstrate that known epistemic ontological models of quantum theory in dimension $d\geq3$, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. We do so by introducing orthogonalizing measurements, which place strict constraints on the structure of epistemic models. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the von Neumann 'cut' under the associated physical "collapse" process.