A Hamiltonian for quantum copying

Abstract

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. 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.