Coexistence of qubit effects

Abstract

We characterize all coexistent pairs of qubit effects. This gives an exhaustive description of all pairs of events allowed, in principle, to occur in a single qubit measurement. The characterization consists of three disjoint conditions which are easy to check for a given pair of effects. Known special cases are shown to follow from our general characterization theorem.

A paper with identical title is being published on the arXiv simultaneously by P. Busch and H.-J. Schmidt. These authors solve the same problem independently with a different method. In v2 the proof of the main result has been clarified, and some minor errors have been corrected. In v3 some typos have been corrected and a reference has been added