Abstract
ψ-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 provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known ψ-epistemic ontological models of quantum theory in dimension d≥3, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. 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 Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness.
Highlights
There are many interpretations of quantum theory1
A third recently articulated category of ψ-doxastic interpretations [25,26,27,28,29,30,31] argue that the quantum state is a state of belief, and are distinguished from ψ-epistemic interpretations by the fact that they deny that a system has some ‘real state.’
We have demonstrated that state update under measurement poses a serious challenge to ψ-epistemic interpretations of quantum theory in the ontological models framework: all currently known ψ-epistemic models for full quantum theory in d ≥ 3 cannot faithfully represent state update
Summary
There are many interpretations of quantum theory. Among the many differences between these interpretations, one that often takes center stage is the stance that they take towards the wavefunction or quantum state. This suggests the possibility that a fully satisfactory ψ-epistemic interpretation cannot explain all of quantum theory despite the qualitatively compelling features of such a view2 This suspicion has led to a number of no-go theorems in recent years which estab-. Despite this motivation, one might still argue that many distinctly quantum phenomena (e.g. Bell inequality violations) can be described without reference to state update; from an operationalist point of view, we shouldn’t need to consider state update in order to investigate these phenomena.
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