Unifying quantum state transfer and state amplification

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.