Quantum Incompatibility in Collective Measurements

Claudio Carmeli, Teiko Heinosaari, Daniel Reitzner, Jussi Schultz and Alessandro Toigo
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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

Mathematics, 2016, vol. 4, issue 3, 1-18

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.

Keywords: quantum incompatibility; collective measurements; joint measurability hypergraphs; noisy spin observables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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