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Quantum Incompatibility in Collective Measurements

Author

Listed:
  • Claudio Carmeli

    (DIME, Università di Genova, Via Magliotto 2, I-17100 Savona, Italy)

  • Teiko Heinosaari

    (Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland)

  • Daniel Reitzner

    (Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia)

  • Jussi Schultz

    (Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland)

  • Alessandro Toigo

    (Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
    I.N.F.N., Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy)

Abstract

We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy separately. We introduce the index of incompatibility as a quantifier of incompatibility in this multi-copy setting, as well as the notion of the compatibility stack representing various compatibility relations present in a given set of observables. We then prove a general structure theorem for multi-copy joint observables and use it to prove that all abstract compatibility stacks with three vertices have realizations in terms of quantum observables.

Suggested Citation

  • Claudio Carmeli & Teiko Heinosaari & Daniel Reitzner & Jussi Schultz & Alessandro Toigo, 2016. "Quantum Incompatibility in Collective Measurements," Mathematics, MDPI, vol. 4(3), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:54-:d:77945
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