Single-particle entanglement and three forms of ambiguity

Abstract

This paper discusses experiments with single-particle systems, some of whose states appear to be entangled. It shows that the interpretation of the experiments in terms of entanglement is ill-defined. Three forms of ambiguity are discussed. The choice of state-space and its dimensions is a matter of taste. There is not an a-priori natural partitioning of the state-space. The observables are not necessarily experimentally accessible and only determined by theory-laden extrapolation from experimental results. These ambiguities need to be addressed in the formulation of any general theory of entanglement.