Identifying and characterizing quantum phases in the presence of long-range correlations and/or spatial disorder is, generally, a challenging and relevant task. Here, we study a generalization of the Kitaev chain with variable-range pairing and different forms of site-dependence of the chemical potantial, addressing commensurate and incommensurate modulations as well as Anderson disorder. In particular, we analyze multipartite entanglement (ME) in the ground state of dirty topological wires by studying the scaling of the quantum Fisher information (QFI) with the system size. For nearest-neighbor pairing, the Heisenberg scaling of the QFI is found in one-to-one correspondence with topological phases hosting Majorana modes. For finite-range pairing, we recognize long-range phases by the superextensive scaling of the QFI and characterize complex lobe-structured phase diagrams. The present work contributes to establish QFI and ME as useful quantities to study intriguing aspects of topological systems, also with long-range pairings and interactions. More generally, our study reports the robustness of spatial multipartite entanglement against spatial inhomogeneities.

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• Quantum Fisher information
• Quantum entanglement
• Disordered systems