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Strongly Incompatible Quantum Devices

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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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  1. This set is equipped with the natural σ-algebra \(\mathcal{F}=2^{\varOmega}\) containing all subsets of Ω. Thus XΩ 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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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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Correspondence to Daniel Reitzner.

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Heinosaari, T., Miyadera, T. & Reitzner, D. Strongly Incompatible Quantum Devices. Found Phys 44, 34–57 (2014).

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