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Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations

Geher, G. and Semrl, P. (2020) Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations. Communications in Mathematical Physics. ISSN 1432-0916 (In Press)

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Abstract/Summary

The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Moln\'ar.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:85685
Publisher:Springer

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