Foundations of Physics

, Volume 44, Issue 1, pp 34–57 | Cite as

Strongly Incompatible Quantum Devices

  • Teiko Heinosaari
  • Takayuki Miyadera
  • Daniel Reitzner


The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.


Quantum measurements Coexistence Joint measurability Compatibility 



T. Heinosaari acknowledges financial support from the Academy of Finland (grant no. 138135). T. Miyadera acknowledges JSPS KAKENHI (grant no. 22740078). D. Reitzner acknowledges financial support from the project COQUIT.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Teiko Heinosaari
    • 1
  • Takayuki Miyadera
    • 2
  • Daniel Reitzner
    • 3
    • 4
  1. 1.Turku Centre for Quantum Physics, Department of Physics and AstronomyUniversity of TurkuTurkuFinland
  2. 2.Department of Nuclear EngineeringKyoto UniversityKyotoJapan
  3. 3.Department of MathematicsTechnische Universität MünchenGarchingGermany
  4. 4.Research Center for Quantum InformationSlovak Academy of SciencesBratislavaSlovakia

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