Dissipation-induced Liouville-Majorana modes in open quantum system

Abstract

In open quantum systems, topological edge states rapidly lose coherence, making them unsuitable for topological quantum computation and quantum memory. In this study, we demonstrate that topologically non-Hermitian Liouville-Majorana edge modes (LMEMs) can persist in the extended Liouville-Fock space (LFS) of dissipative quantum spin or fermionic systems. This finding extends the scope of topological modes beyond typical Hermitian systems. By vectorizing the Lindblad equation of a dissipative Ising-type spin system using third quantization, we prove that it can be reduced to a series of non-Hermitian Kitaev chains in the extended LFS and that topologically protected LMEMs emerge due to internal symmetry. Furthermore, we present an explicit method for detecting these modes and demonstrate that the purity of the density matrix characterizes the long-range correlation of LMEMs. Our work offers a new direction for identifying stable topological states in open quantum systems induced by quantum jumps.