  We present a detailed study on the possibility of manipulating quantum
information encoded in the "radial" modes of arrays of trapped ions (i.e., in
the ions' oscillations orthogonal to the trap's main axis). In such systems,
because of the tightness of transverse confinement, the radial modes pertaining
to different ions can be addressed individually. In the first part of the paper
we show that, if local control of the radial trapping frequencies is available,
any linear optical and squeezing operation on the locally defined modes - on
single as well as on many modes - can be reproduced by manipulating the
frequencies. Then, we proceed to describe schemes apt to generate unprecedented
degrees of bipartite and multipartite continuous variable entanglement under
realistic noisy working conditions, and even restricting only to a global
control of the trapping frequencies. Furthermore, we consider the transmission
of the quantum information encoded in the radial modes along the array of ions,
and show it to be possible to a remarkable degree of accuracy, for both
finite-dimensional and continuous variable quantum states. Finally, as an
application, we show that the states which can be generated in this setting
allow for the violation of multipartite non-locality tests, by feasible
displaced parity measurements. Such a demonstration would be a first test of
quantum non-locality for "massive" degrees of freedom (i.e., for degrees of
freedom describing the motion of massive particles).
