Coexistence of qubit effects

TL;DR

This paper characterizes when two effects in a qubit system can be measured together, using Minkowski space geometry to provide multiple equivalent conditions for coexistence.

Contribution

It offers new geometric characterizations of coexistent qubit effects and links these results with existing independent findings.

Findings

Multiple equivalent conditions for coexistence of qubit effects

Use of Minkowski space geometry in effect analysis

Establishment of correspondence with previous results

Abstract

Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space.