  Recently there have been numerous proposals to create Majorana zero modes in
solid state heterojunctions, superconducting wires and optical lattices.
Putatively the information stored in qubits constructed from these modes is
protected from various forms of decoherence. Here we show that this is not the
case. We present a generic method to study the effect of external perturbations
on these modes. We focus on the case where there are no interactions between
different Majorana modes either directly or through intermediary fermions. To
quantify the rate of loss of the information stored in the Majorana modes we
study the two-time correlators for qubits built from them. We analyze a generic
gapped fermionic environment (bath) interacting via tunneling with different
components of the qubit (different Majorana modes). We find that static
(time-independent) perturbations are not harmful, and just lead to a depletion
of the information stored that saturates in the long-time limit. On the other
hand we find markedly different results for dynamic (time dependent) systems,
with no coherence surviving in the long time limit. In particular we find that
dephasing and energy fluctuations of the modes in the fermionic bath have
adverse effects on the Majorana memories.
