  We develop a theoretical scheme to perform a read-out of the properties of a
quasi-periodic system by coupling it to one or two qubits. We show that the
decoherence dynamics of a single qubit coupled via a pure dephasing type term
to a 1D quasi-periodic system with a potential given by the
Andr\'e-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is
sensitive to the nature of the single particle eigenstates (SPEs). More
specifically, we can use the non-markovianity of the qubit dynamics as
quantified by the backflow of information to clearly distinguish the localized,
delocalized, and mixed regimes with a mobility edge of the AAH and GAAH model
and evidence the transition between them. By attaching two qubits at distinct
sites of the system, we demonstrate that the transport property of the
quasi-periodic system is encoded in the scaling of the threshold time to
develop correlations between the qubits with the distance between the qubits.
This scaling can also be used to distinguish and infer different regimes of
transport such as ballistic, diffusive and no transport engendered by SPEs that
are delocalized, critical and localized respectively. When there is a mobility
edge allowing the coexistence of different kinds of SPEs in the spectrum, such
as the coexistence of localized and delocalized states in the GAAH models, we
find that the transport behaviour and the scaling of the threshold time with
qubit separation is governed by the fastest spreading states.
