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Article

Quantum Incompatibility in Collective Measurements

1
DIME, Università di Genova, Via Magliotto 2, I-17100 Savona, Italy
2
Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
3
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
4
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
5
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
Mathematics 2016, 4(3), 54; https://doi.org/10.3390/math4030054
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)
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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MDPI and ACS Style

Carmeli, C.; Heinosaari, T.; Reitzner, D.; Schultz, J.; Toigo, A. Quantum Incompatibility in Collective Measurements. Mathematics 2016, 4, 54. https://doi.org/10.3390/math4030054

AMA Style

Carmeli C, Heinosaari T, Reitzner D, Schultz J, Toigo A. Quantum Incompatibility in Collective Measurements. Mathematics. 2016; 4(3):54. https://doi.org/10.3390/math4030054

Chicago/Turabian Style

Carmeli, Claudio; Heinosaari, Teiko; Reitzner, Daniel; Schultz, Jussi; Toigo, Alessandro. 2016. "Quantum Incompatibility in Collective Measurements" Mathematics 4, no. 3: 54. https://doi.org/10.3390/math4030054

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