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Semiconducting nanowires with strong Rashba spin-orbit coupling in theproximity with a superconductor and under a strong Zeeman field can potentiallymanifest Majorana zero modes at their edges and are a topical candidate fortopological superconductivity. However, protocols for their detection based onthe local and the non-local conductance spectroscopy have been subject tointense scrutiny. In this work, by taking current experimental setups intoaccount, we detail mathematical ideas related to the entanglement entropy andthe fermion parity fluctuations to faithfully distinguish between true Majoranazero modes and trivial quasi-Majorana zero modes. We demonstrate that thedisconnected entanglement entropy, derived from the von Neumann entanglemententropy, provides a distinct and robust signature of the topological phasetransition which is immune to system parameters, size and disorders. In orderto understand the entanglement entropy of the Rashba nanowire system, weestablish its connection to a model of interacting spinfull Kitaev chains.Moreover, we relate the entanglement entropy to the fermionic parityfluctuation, and show that it behaves concordantly with entanglement entropy,hence making it a suitable metric for the detection of Majorana zero modes. Inconnection with the topological gap protocol that is based on the conductancespectra, the aforesaid metrics can reliably point toward the topologicaltransitions even in realistic setups.

On the conclusive detection of Majorana zero modes: conductance spectroscopy, disconnected entanglement entropy and the fermion parity noise