Coexistence of qubit effects

Paul Busch, Heinz-Jürgen Schmidt

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)143-169
Number of pages26
JournalQuantum Information Processing
Issue number2
Publication statusPublished - Apr 2010

Bibliographical note

© Springer Science+Business Media, LLC 2009. This is an author produced version of a paper published in 'Quantum Information Processing'. Uploaded in accordance with the publisher's self-archiving policy.


  • quantum observables
  • joint measurability
  • coexistence
  • qubit

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