  The local convertibility of quantum states, measured by the R\'enyi entropy,
is concerned with whether or not 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.
