  Understanding the physical significance and probing the global invariants
characterizing quantum topological phases in extended systems is a main
challenge in modern physics with major impact in different areas of science.
Here, a quantum-information-inspired probing method is proposed where
topological phase transitions are revealed by a non-Markovianity quantifier.
The idea is illustrated by considering the decoherence dynamics of an external
read-out qubit that probes a Su-Schrieffer-Heeger (SSH) chain with either pure
dephasing or dissipative coupling. Qubit decoherence features and
non-Markovianity measure clearly signal the topological phase transition of the
SSH chain.
