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Almost Sharp Quantum Effects Alvaro Arias and Stan Gudder

Summary: Almost Sharp Quantum Effects
Alvaro Arias and Stan Gudder
Department of Mathematics
The University of Denver
Denver, Colorado 80208
April 15, 2004
Quantum effects are represented by operators on a Hilbert space satis-
fying 0 A I, and sharp quantum effects are represented by projection
operators. We say that an effect A is almost sharp if A = PQP for projec-
tions P and Q. We give simple characterizations of almost sharp effects.
We also characterize effects that can be written as longer products of pro-
jections. For generality we first work in the formalism of von Neumann
algebras. We then specialize to the full operator algebra B (H) and to
finite dimensional Hilbert spaces.
1 Introduction
Let H be a complex Hilbert space that represents the state space of a quantum
system S. The set of effects E (H) for S is the set of operators on H satisfying 0
A I. Effects represent yes-no measurements that may be unsharp (imprecise,
fuzzy). It is interesting that many of the important classes of quantum operators


Source: Arias, Alvaro - Department of Mathematics, University of Denver


Collections: Mathematics