  The quantum mechanical transition probability is symmetric. A
probabilistically motivated and more general quantum logical definition of the
transition probability was introduced in two preceding papers without
postulating its symmetry, but in all the examples considered there it remains
symmetric. Here we present a class of binary models where the transition
probability is not symmetric, using the extreme points of the unit interval in
an order unit space as quantum logic. We show that their state spaces are
strictly convex smooth compact convex sets and that each such set K gives rise
to a quantum logic of this class with the state space K. The transition
probabilities are symmetric iff K is the unit ball in a Hilbert space. In this
case, the quantum logic becomes identical with the projection lattice in a spin
factor which is a special type of formally real Jordan algebra.
