  To study various quantum dynamics, it is important to develop effective
methods to detect and distinguish different quantum dynamics. A common
non-demolition approach is to couple an auxiliary system (ancilla) to the
target system, and to measure the ancilla only. By doing so, the target system
becomes an environment for the ancilla. Thus, different quantum dynamics of
target systems will correspond to different environment properties. Here, we
analytically study XX spin chains presenting different kinds of quantum
dynamics, namely localized, delocalized, and dephasing dynamics, and build
connections between Markovianity and non-Markovianity - the two most common
properties of an environment. For a qubit coupled to the XX chain, we derived
the reduced density matrix of the qubit through the projection method.
Furthermore, when dephasing noise was introduced to the XX chain, we
generalized the projection method by introducing an open-system interaction
picture - a modification of the Dirac interaction picture. By calculating the
reduced density matrix for the qubit analytically and numerically, we found
that the delocalized (localized) chain corresponds to the Markovian
(non-Markovian) bath when boundary effects are not considered, and the feature
of the chain with dephasing noise as a bath is dependent on the dephasing
strength. The three kinds of quantum dynamics can be distinguished by measuring
the qubit only.
