Breakdown of local convertibility through Majorana modes in a quantum quench

TL;DR

This paper investigates how local convertibility of quantum states in a Kitaev chain depends on quantum phases and Majorana edge modes, revealing conditions for inconvertibility related to topological properties.

Contribution

It demonstrates the dependence of local convertibility on quantum phases and edge modes in a quenched Kitaev chain, providing physical insights into topological entanglement.

Findings

Edge modes lead to local inconvertibility for large subsystems.

Convertibility depends on the quantum phase and subsystem size.

Physical interpretation based on subsystem interactions is provided.

Abstract

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.