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

Geher, G. P. and Semrl, P. (2020) Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations. Communications in Mathematical Physics, 379. pp. 1077-1112. ISSN 1432-0916 doi: 10.1007/s00220-020-03873-3

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 Molnar.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/85685
Identification Number/DOI	10.1007/s00220-020-03873-3
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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