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On the notion of coexistence in quantum mechanics

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Mathematica Slovaca

Abstract

The notion of coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements.

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Authors and Affiliations

  1. University of York, York, YO10 5DD, UK

    Paul Busch

  2. Institut für Theoretische Physik, Universität Hannover, D-30167, Hannover, Germany

    Jukka Kiukas

  3. Turku Center for Quantum Physics Department of Physics and Astronomy, University of Turku, FIN-20014, Turku, Finland

    Pekka Lahti

Authors
  1. Paul Busch
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  2. Jukka Kiukas
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  3. Pekka Lahti
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Correspondence to Paul Busch.

Additional information

Communicated by Anatolij Dvurečenskij

Dedicated to Professor Sylvia Pulmannová on the occasion of her 70th birthday

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Busch, P., Kiukas, J. & Lahti, P. On the notion of coexistence in quantum mechanics. Math. Slovaca 60, 665–680 (2010). https://doi.org/10.2478/s12175-010-0039-1

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  • DOI: https://doi.org/10.2478/s12175-010-0039-1

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