operate on a classical probabilistic bit.
Such a binary system is described by
a two-dimensional vector of probabilities, corresponding to the probability p0 of being in 0 and p1 of being
in 1. The operations I and X can then
be represented on this system as the
In group theoretic parlance, we say that
these two matrices form a
representation of the group, which effectively
means that the multiplication among
these matrices mimics the operation
among the elements of the group that
is being represented.