  We consider a bipartite transformation that we call self-embezzlement and use
it to prove a constant gap between the capabilities of two models of quantum
information: the conventional model, where bipartite systems are represented by
tensor products of Hilbert spaces; and a natural model of quantum information
processing for abstract states on C*-algebras, where joint systems are
represented by tensor products of C*-algebras. We call this the C*-circuit
model and show that it is a special case of the commuting-operator model (in
that it can be translated into such a model). For the conventional model, we
show that there exists a constant $\epsilon_0 > 0$ such that self-embezzlement
cannot be achieved with precision parameter less than $\epsilon_0$ (i.e., the
fidelity cannot be greater than $1 - \epsilon_0$); whereas, in the C*-circuit
model -- as well as in a commuting-operator model -- the precision can be $0$
(i.e., fidelity~$1$).
