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Strongly Incompatible Quantum Devices

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Abstract

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.

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Notes

  1. This set is equipped with the natural σ-algebra \(\mathcal{F}=2^{\varOmega}\) containing all subsets of Ω. Thus X⊆Ω is equivalent to \(X\in\mathcal{F}\) in this paper, while the latter should be employed in treating infinite outcome set Ω.

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Acknowledgements

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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Authors and Affiliations

  1. Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, Turku, Finland

    Teiko Heinosaari

  2. Department of Nuclear Engineering, Kyoto University, 6158540, Kyoto, Japan

    Takayuki Miyadera

  3. Department of Mathematics, Technische Universität München, 85748, Garching, Germany

    Daniel Reitzner

  4. Research Center for Quantum Information, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia

    Daniel Reitzner

Authors
  1. Teiko Heinosaari
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  2. Takayuki Miyadera
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  3. Daniel Reitzner
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Correspondence to Daniel Reitzner.

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Heinosaari, T., Miyadera, T. & Reitzner, D. Strongly Incompatible Quantum Devices. Found Phys 44, 34–57 (2014). https://doi.org/10.1007/s10701-013-9761-1

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  • DOI: https://doi.org/10.1007/s10701-013-9761-1

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