Quantum Information Processing

, Volume 9, Issue 2, pp 143–169

Coexistence of qubit effects

Authors

    • Department of MathematicsUniversity of York
  • Heinz-Jürgen Schmidt
    • Fachbereich PhysikUniversität Osnabrück
Article

DOI: 10.1007/s11128-009-0109-x

Cite this article as:
Busch, P. & Schmidt, H. Quantum Inf Process (2010) 9: 143. doi:10.1007/s11128-009-0109-x

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.

Keywords

Qubit Effect Joint measurability Coexistence Unsharp observable

PACS

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

Copyright information

© Springer Science+Business Media, LLC 2009