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Mathematics 2016, 4(3), 54;

Quantum Incompatibility in Collective Measurements

DIME, Università di Genova, Via Magliotto 2, I-17100 Savona, Italy
Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
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
Author to whom correspondence should be addressed.
Academic Editors: Paul Busch and Takayuki Miyadera
Received: 29 March 2016 / Revised: 1 September 2016 / Accepted: 3 September 2016 / Published: 10 September 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
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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. View Full-Text
Keywords: quantum incompatibility; collective measurements; joint measurability hypergraphs; noisy spin observables quantum incompatibility; collective measurements; joint measurability hypergraphs; noisy spin observables

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Carmeli, C.; Heinosaari, T.; Reitzner, D.; Schultz, J.; Toigo, A. Quantum Incompatibility in Collective Measurements. Mathematics 2016, 4, 54.

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