Universal control of quantum subspaces and subsystems
Paolo Zanardi, Seth Lloyd · Physical Review A · 2004
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are found in terms of the representation theory of the group ${\mathcal{U}}_{A}$ of allowed quantum evolutions. In some cases universal control can be achieved in all the state-space sectors carrying an irreducible action of ${\mathcal{U}}_{A}.$ All known physical examples of universal control on subspaces/systems are related to the framework developed here. Implications for quantum-information processing are discussed.