Persistence of topological phases in non-Hermitian quantum walks

Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact PT-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the PT-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.

Automated summary

The research shows that the topological phases of quantum walks remain relatively robust even in a lossy environment. In one-dimensional split-step quantum walks, the topological order persists as long as the Hamiltonian maintains exact PT-symmetry, while in two-dimensional quantum walks, PT-symmetry plays no role and losses may induce a topological phase transition.