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arXiv · 1605.07551

Quantum incompatibility in collective measurements

Claudio Carmeli·Teiko Heinosaari·Daniel Reitzner·Jussi Schultz·Alessandro Toigo
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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 compatibility stack representing the 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.

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Claudio Carmeli, Teiko Heinosaari, Daniel Reitzner, Jussi Schultz, Alessandro Toigo. 2016-05-24. Quantum incompatibility in collective measurements. https://doi.org/10.3390/math4030054

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