Universal two-time correlations, out-of-time-ordered correlators and Leggett-Garg inequality violation by edge Majorana fermion qubits

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.