Breakdown of local convertibility through Majorana modes in a quantum quench

The local convertibility of quantum states, measured by the Renyi entropy, is concerned with whether a state can be transformed into another state, using only local operations and classical communications. We found that in the one-dimensional Kitaev chain with quenched chemical potential mu, the convertibility between the state for mu and that for mu + delta mu depends on the quantum phases of the system (delta mu is a perturbation). This is similar to the adiabatic case where the ground state is considered. Specifically, when the quenched system has edge modes and the subsystem size for the partition is much larger than the correlation length of the Majorana fermions which forms the edge modes, the quenched state is locally inconvertible. We give a physical interpretation for the result, based on analyzing the interactions between the two subsystems for various partitions. Our work should help to better understand the many-body phenomena in topological systems and also the entanglement properties in the Majorana fermionic quantum computation.