Thermal quantum information capacity in a topological insulator

Thermal effects in a one-dimensional Su-Schrieffer-Hegger topological insulator are studied. Particularly, we focus on quantum information processing capacity for thermal ensembles. To evaluate quantum information processing, an optimized quantum Fisher information is introduced as a quantifier of entanglement and topological phases are calculated by a definition in real space for the electric polarization of mixture states. For the thermal ensemble, there is a relationship between the Fisher metric and the electric polarization in such a way that in the topological region, there is more entanglement, and therefore, creates more robustness and protection in the quantum information against to thermal effects. Moreover, long-range hopping effects are studied and it is found that in this case, the optimized quantum Fisher information captures these topological phase transitions in the limit of low temperature by the formalism in real space.