  The Uhlmann connection is a mixed state generalisation of the Berry
connection. The latter has a very important role in the study of topological
phases at zero temperature. Closely related, the quantum fidelity is an
information theoretical quantity which is a measure of distinguishability of
quantum states. Moreover, it has been extensively used in the analysis of
quantum phase transitions. In this work, we study topological phase transitions
in 1D and 2D topological superconductors with long-range hopping and pairing
amplitudes, using the fidelity and the quantity $\Delta$ closely related to the
Uhlmann connection. The drop in the fidelity and the departure of $\Delta$ from
zero signal the topological phase transitions in the models considered. The
analysis of the ground state fidelity susceptibility and its associated
critical exponents are also applied to the study of the aforementioned
topological phase transitions.
