Coexistence of qubit effects

TL;DR

This paper provides a complete characterization of all pairs of qubit effects that can coexist in a single measurement, offering a comprehensive and easily checkable set of conditions.

Contribution

It introduces a general theorem that exhaustively describes coexistent qubit effects, unifying known special cases under a single framework.

Findings

Complete characterization of coexistent qubit effects

Three disjoint conditions for coexistence

Simplified criteria for checking effect pairs

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.