Ali Leylani: The inability of Spekkens’ epistemic view of quantum states to reproduce the solution to the mean king’s problem

Abstract: For the significant part of the past century, the familiar Copenhagen interpretation, an inherently proba- bilistic stance, has been the dominant vantage point for research on quantum mechanics. Lately, however, new experimental results once again fuel debate and contending interpretations make their claim. Most notably, perhaps, being the pilot wave formulation, an inherently deterministic viewpoint. A recurring, more specific, front of this debate is whether quantum mechanics behaves in a manner described by an ontic or an epistemic theory. Spekkens, to the defence of the latter, outlines in his paper [1] a toy theory explicitly rooted in a belief that there exists fundamental limits to an observers knowledge of a particle’s state. The argument the author, very reasonably, makes for epistemology is that an extension of the pile of experiments covered and explained by it, while failing for the contenders, continuously adds to its plausibility. In this paper, however, we present a failure of the toy theory to replicate the solution to the mean king’s problem as presented by Vaidman, Aharonov and Albert [2]. Strictly speaking, this is not evidence against all of epistemology, rather an argument only against this toy theory which sets a seemingly arbitrary restriction on its foundation. A restriction Spekkens refers to as the knowledge balance principle