TESTING STATISTICAL HYPOTHESES IN QUANTUM THEORY
Abstract: The paper presents an account of quantum hypotheses testing theory and the new
contributions clarifying the role of orthogonal resolutions of identity (simple measurements)
in the quantum Bayes problem. It is shown that the maximum likelihood measurement is
simple for the family of states with linearly independent ranges. This is an extension of
Kennedy’s result for the pure states. A counterexample to an old physical conjecture is
constructed showing that in the Bayes problem with the total number of decisions less than or
equal to the dimension of the underlying Hilbert space the Bayes measurement may not be
simple. However, it is shown that in the infinite-dimensional case there always exists an
-Bayes simple measurement.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -