  In the present work we propose that two-time correlations of Majorana edge
localized fermions constitute a novel and versatile toolbox for assessing the
topological phases of 1D open lattices. Using analytical and numerical
calculations on the Kitaev model, we uncover universal relationships between
the decay of the short-time correlations and a particular family of
out-of-time-ordered correlators, which provide direct experimental alternatives
to the quantitative analysis of the system regime, either normal or
topological. Furthermore we show that the saturation of two-time correlations
possesses features of an order parameter. Finally, we find that violations of
Leggett-Garg inequalities can indicate the topological-normal phase transition
by looking at different qubits formed by pairing local and non-local edge
Majorana fermions.
