The Phenomenological Preparation - Registration Arrow of Time and its   Semigroup Representation in the RHS Quantum Theory
  The observed probabilities of quantum mechanics possess a time asymmetry which is based on the truism that a state must be prepared before an observable can be measured in it. While Hilbert space quantum theory cannot incorporate this arrow of time, the Rigged Hilbert Space (RHS) formulation of quantum mechanics provides a theory of time symmetric as well as time asymmetric quantum physics. 
Arno R. Bohm, Raymond Scurek