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

Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement