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      Sequential product of quantum effects

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      Author
      Gheondea, A.
      Gudder, S.
      Date
      2004
      Source 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
      Article
      Item Usage Stats
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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.
      Permalink
      http://hdl.handle.net/11693/27469
      Published Version (Please cite this version)
      http://dx.doi.org/10.1090/S0002-9939-03-07063-1
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