we learned from the description of the us 1945 5205 cryptographic process how, despite all its engineering complexity, the machine counted how many time certain (high scoring, distinguishing) characters appeared in a tunny stream. for example, compute chi (5bits) xor ‘e’ (5 bits). now count the hits in cipher. e will have less uncertainty than it would have, were its to be found in a random cipher stream.
we have seen that, in quantum mechanics, a inner product is, on the one hand, a measure of the distinguishability of two states, and ‘the value e’ on the other. Should one score ‘e’, its a measure of the transition probability. perhaps e is just a representative of its weight class, and perhaps one goes about counting any distinction equivalent to a weight difference.