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Sequential quantum measurements
by
Aurelian Gheondea
Institute of Mathematics of the Romanian Academy
Coauthors: S.P. Gudder
Unsharp quantum measurements can be modelled by means of the class E(H) of positive contractions on a Hilbert space H. For A, B in E(H) the operation of sequential product A o B=A1/2BA1/2 was proposed as a model for sequential quantum measurements. This paper answers two questions.
The first one asks whether the assumption A o B >= B implies AB=BA=B. In terms of quantum measurements this means that we cannot amplify an effect by preceding it with another effect. This is known to be true for finite dimensional Hilbert spaces, cf. G. Nagy and S.P. Gudder, and we prove that it is true for infinite dimensional Hilbert spaces as well.
The second question is related to 2×2 matrix representation of quantum effects in terms of free objects. We use the well known 2×2 matrix representation and the infimum problem for positive operators, to obtain an answer in some special cases. This provides an approach with operator ranges and parallel sum for quantum effects.
Date received: May 29, 2002
Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-34.