  The aim of this paper is to introduce a new graphic representation of quantum
states by means of a specific application: the analysis of two models of
quantum copying machines. The graphic representation by diagrams of states
offers a clear and detailed visualization of quantum information's flow during
the unitary evolution of not too complex systems. The diagrams of states are
exponentially more complex in respect to the standard representation and this
clearly illustrates the discrepancy of computational power between quantum and
classical systems. After a brief introductive exposure of the general theory,
we present a constructive procedure to illustrate the new representation by
means of concrete examples. Elementary diagrams of states for single-qubit and
two-qubit systems and a simple scheme to represent entangled states are
presented. Quantum copying machines as imperfect cloners of quantum states are
introduced and the quantum copying machines of Griffiths and Niu and of Buzek
and Hillery are analyzed, determining quantum circuits of easier
interpretation. The method has indeed shown itself to be extremely successful
for the representation of the involved quantum operations and it has allowed to
point out the characteristic aspects of the quantum computations examined.
