Letters in Mathematical Physics

, Volume 105, Issue 5, pp 661–673 | Cite as

Compatibility Properties of Extreme Quantum Observables

  • Erkka HaapasaloEmail author
  • Juha-Pekka Pellonpää
  • Roope Uola


Recently, a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved (Reeb at al. J Phys A Math Theor 46:462002, 2013). In this paper, we generalize two known joint measurability results from sharp observables to the class of extreme observables and study relationships between coexistence, joint measurability, and post-processing of quantum observables when an extreme observable is involved. We also discuss another notion of compatibility and provide a counterexample separating this from the former notions.


positive operator-valued measure joint measurability coexistence extremality 

Mathematics Subject Classification

81P45 81Q99 46N10 46N50 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Erkka Haapasalo
    • 1
    Email author
  • Juha-Pekka Pellonpää
    • 1
  • Roope Uola
    • 1
    • 2
  1. 1.Department of Physics and Astronomy, Turku Centre for Quantum PhysicsUniversity of TurkuTurkuFinland
  2. 2.Naturwissenschaftlich-Technische FakultätUniversität SiegenSiegenGermany

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