Quantum information spreading in random spin chains with topological order

Quantum information spreading and scrambling in many-body systems attract interest these days. Tripartite mutual (TMI) based on operator-based entanglement entropy (EE) is an efficient tool for measuring them. In this paper, we study random spin chains that exhibit phase transitions accompanying nontrivial changes topological properties. their diagrams, there are two types of localized (MBL) states one thermalized regime intervening MBL states. Quench dynamics the EE TMI display interesting behaviors, providing essential perspective concerning encoding quantum information. particular, models self-dual, but measured by does not respect self-duality. We investigate phenomenon from viewpoint spatial structure stabilizers. general, find knowledge diagram corresponding to qubit system useful understanding nature system. The connection between present paper circuit projective measurements also Majorana memory remarked upon.