  In non-Hermitian quasicrystals, mobility edges (ME) separating localized and
extended states in complex energy plane can arise as a result of non-Hermitian
terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies
of localized and extended states exhibit distinct topological structures in the
complex energy plane. However, depending on the origin of non-Hermiticity, i.e.
asymmetry of hopping amplitudes or complexification of the incommensurate
potential phase, different winding numbers are introduced, corresponding to
different transport features in the bulk of the lattice: while ballistic
transport is allowed in the former case, pseudo dynamical localization is
observed in the latter case. The results are illustrated by considering
non-Hermitian photonic quantum walks in synthetic mesh lattices.
