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 $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -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.