Quantum Information Processing

, Volume 9, Issue 2, pp 143-169

First online:

Coexistence of qubit effects

  • Paul BuschAffiliated withDepartment of Mathematics, University of York Email author 
  • , Heinz-Jürgen SchmidtAffiliated withFachbereich Physik, Universität Osnabrück

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.


Qubit Effect Joint measurability Coexistence Unsharp observable


03.65.Ta 03.67.-a 02.30.Tb 02.40.Ft