Long-lasting Topological Entanglement in a Monitored Rashba Nanowire
We study the topological properties of a monitored Rashba chain along quantum-jump trajectories, investigating the persistence of the initial topological value of the disconnected entanglement entropy (DEE). We find that the DEE persists in its topological value for a time linear in the system size, even if the dissipation acts on the boundary and affects the topological Majorana modes. The reason for this phenomenon lies in the absence of particle conservation and in the degeneracy of the topological manifold, allowing the monitoring to let the system switch between different topological states -- alternatively creating and annihilating a Majorana mode -- while producing a poisoning of finite-energy ballistically propagating quasiparticles that eventually destroy the topological entanglement structure.