We investigate for quantum dynamics in phase-space regions containing ``shearless tori. We show that the properties of these peculiar classical phase-space structures -- important to the dynamics of tokamaks -- may be exploited for quantum information applications. In particular we show that shearless tori permit the non-dispersive transmission of localized wavepackets. The quantum many-body Hamiltonian of a Heisenberg ferromagnetic spin chain, subjected to an oscillating magnetic field, can be reduced to a classical one-body ``image dynamical system which is the well-studied Harper map. The Harper map belongs to a class of Hamiltonian systems (non-twist maps) which contain shearless tori. We show that a variant with sinusoidal time driving ``driven Harper model produces shearless tori which are especially suitable for quantum state transfer. The behavior of the concurrence is investigated as an example.
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