A HAMILTONIAN FOR QUANTUM COPYING

We derive an explicit Hamiltonian for copying the basis up and down st ates of a quantum two-state system - a qubit - onto n ''copy'' qubits (n greater than or equal to 1) initially all prepared in the down stat e. In terms of spin components, for spin-1/2 particle spin states, the resulting Hamiltonian involves n- and (n + 1)-spin interactions. The case n = 1 also corresponds to a quantum-computing controlled-NOT gate .