A Hamiltonian for Quantum Copying
Dima Mozyrsky, Vladimir Privman, Mark Hillery · 1996
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 (n ≥ 1) 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. PACS numbers: 03.65.Bz, 85.30.St. – 1 – Interest in quantum computing [1-27] has boosted studies of quantum mechanics of two-state systems such as the spin states of spin- 1 2 particles. We will use “spin ” to indicate a two-state system in this context. The “binary ” up and down spin states are of particular significance and