We can perform an observation, which irreversibly collapses the system into some eigenstate of an observable, corrupting the information contained in the qubit(s). This is obviously not what we want. Alternatively, we could control the Hamiltonian of the combined system, and thus the time-evolution operator U(t), e.g. for a time-independent Hamiltonian, Evolving up to some fixed time yields a unitary operator U on the Hilbert space of the combined system. However, no such unitary operator U can clone all states.
We can perform an observation, which irreversibly collapses the system into some eigenstate of an observable, corrupting the information contained in the qubit(s). This is obviously not what we want. Alternatively we could control the Hamiltonian of the combined system, and thus the time-evolution operator U(t), e.g. for a time-independent Hamiltonian, Evolving up to some fixed time yields a unitary operator U on the Hilbert space of the combined system. However, no such unitary operator U can clone all states.