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For many quantum information protocols such as state transfer, entanglementtransfer and entanglement generation, standard notions of controllability forquantum systems are too strong. We introduce the weaker notion of accessiblepairs, and prove an upper bound on the achievable fidelity of a transformationbetween a pair of states based on the symmetries of the system. A large classof spin networks is presented for which this bound can be saturated. In thiscontext, we show how the inaccessible dark states for a givenexcitation-preserving evolution can be calculated, and illustrate how some ofthese can be accessed using extra catalytic excitations. This emphasises thatit is not sufficient for analyses of state transfer in spin networks torestrict to the single excitation subspace. One class of symmetries in thesespin networks is exactly characterised in terms of the underlying graphproperties.

Quantum Control Theory for State Transformations: Dark States and their Enlightenment