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Reduction and Extremality of Finite Observables

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We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one observables and consider various constructions that reduce observables to simpler ones. However, these constructions do not suffice to generate all finite extremal observables, as we show by means of counter-examples.

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Acknowledgements

An early version of this paper war co-authored by Paul Busch. Due to his untimely passing away we were not able to finish it as a joint paper. Therefore I have to publish it under my sole responsibility but simultaneously I gratefully acknowledge his essential contributions and, more generally, his continuous support and encouragement for research on fundamental questions of quantum theory. The community has lost a profound scholar and a person of integrity.

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  1. Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany

    Heinz-Jürgen Schmidt

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  1. Heinz-Jürgen Schmidt
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Correspondence to Heinz-Jürgen Schmidt.

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Schmidt, HJ. Reduction and Extremality of Finite Observables. Found Phys 49, 577–593 (2019). https://doi.org/10.1007/s10701-019-00259-x

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