  In order to increase the coherence time of topological quantum memories in
systems with Majorana zero modes, it has recently been proposed to encode the
logical qubit states in non-local Majorana operators which are immune to
localized excitations involving the unpaired Majorana modes. In this encoding,
a logical error only happens when the quasi-particles, subsequent to their
excitation, travel a distance of the order of the spacing between the Majorana
modes. Here, we study the decay time of a quantum memory encoded in a clean
topological nanowire interacting with an environment with a particular emphasis
on the propagation of the quasi-particles above the gap. We show that the
non-local encoding does not provide a significantly longer coherence time than
the local encoding. In particular, the characteristic speed of propagation is
of the order of the Fermi velocity of the nanowire and not given by the much
slower group velocity of quasi-particles which are excited just above the gap.
