Signatures of Majorana zero-modes in a fusion experiment and beyond

In most cases, the signatures of the Majorana zero-modes (MZMs) in class D systems (e.g. in topological superconductors) can be mimicked by the sub-gap states with energy close to zero (so-called Andreev levels). I will demonstrate it on the example of the Majorana fusion experiment that is believed to be an easier way to demonstrate the non-Abelian statistics of Majoranas as compared to braiding. After explaining the fundamental underlying reason of why it happens, I will propose the dynamical signature that is the defining property of non-Abelian anyons and that can discriminate against accidental Andreev levels.