Sequential product of quantum effects
Author
Gheondea, A.
Gudder, S.
Date
2004Source Title
Proceedings of the American Mathematical Society
Print ISSN
0002-9939
Electronic ISSN
1088-6826
Publisher
American Mathematical Society
Volume
132
Issue
2
Pages
503 - 512
Language
English
Type
ArticleItem Usage Stats
119
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Abstract
Unsharp quantum measurements can be modelled by means of the class ℰ(ℋ) of positive contractions on a Hilbert space ℋ, in brief, quantum effects. For A, B ∈ ℰ(ℋ) the operation of sequential product AοB = A1/2 BA1/2 was proposed as a model for sequential quantum measurements. We continue these investigations on sequential product and answer positively the following question: the assumption AοB ≥ B implies AB = BA = B. Then we propose a geometric approach of quantum effects and their sequential product by means of contractively contained Hilbert spaces and operator ranges. This framework leads us naturally to consider lattice properties of quantum effects, sums and intersections, and to prove that the sequential product is left distributive with respect to the intersection.