  A witness of non-Markovianity based on the Hilbert-Schmidt speed (HSS), a
special type of quantum statistical speed, has been recently introduced for
low-dimensional quantum systems. Such a non-Markovianity witness is
particularly useful, being easily computable since no diagonalization of the
system density matrix is required. We investigate the sensitivity of this
HSS-based witness to detect non-Markovianity in various high-dimensional and
multipartite open quantum systems. We find that the time behaviors of the
HSS-based witness are always in agreement with those of quantum negativity or
quantum correlation measure. These results show that the HSS-based witness is a
faithful identifier of the memory effects appearing in the quantum evolution of
a high-dimensional system.
