Single-particle entanglement and three forms of ambiguity

TL;DR

This paper critically examines the interpretation of single-particle experiments claiming entanglement, highlighting ambiguities in state-space choice, observable accessibility, and the need for clearer theoretical foundations.

Contribution

It identifies three key ambiguities in interpreting single-particle entanglement experiments and emphasizes their importance for developing a consistent theory of entanglement.

Findings

Interpretation of single-particle entanglement is ill-defined.

Choice of state-space and dimensions is subjective.

Observables are often theory-laden and not directly accessible.

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.