 Consider the automaton to be in a state formula_22.After reading an input letter formula_30, the automaton will be in the state

At this point, a measurement is performed on the state formula_32, using the projection operators formula_36, at which time its wave-function collapses into one of the three subspaces formula_83 or formula_84 or formula_85.The probability of collapse is given by

for the "accept" subspace, and analogously for the other two spaces.