Topological phase transitions and edge-state transfer in time-multiplexed quantum walks

We investigate the topological phase transitions and edge-state properties of a time-multiplexed nonunitary quantum walk with sublattice symmetry. By constructing a Floquet operator incorporating tunable gain and loss, we systematically analyze both unitary and nonunitary regimes. In the unitary case, the conventional bulk-boundary correspondence (BBC) is preserved, with edge modes localized at opposite boundaries as predicted by topological invariants. In contrast, the nonunitary regime exhibits non-Hermitian skin effects, leading to a breakdown of the conventional BBC. By applying non-Bloch band theory and generalized Brillouin zones, we restore a generalized BBC and reveal a transfer phenomenon, where edge modes with different sublattice symmetries can become localized at the same boundary. Furthermore, we demonstrate that the structure of the spectral loops in the complex quasienergy plane provides a clear signature for these transfer behaviors. Our findings deepen the understanding of nonunitary topological phases and offer valuable insights for the experimental realization and control of edge states in non-Hermitian quantum systems.