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Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder

We present a statistical analysis on the performance of a protocol for the faithful transfer of a quantum state in finite qubit or spin chains, in the presence of diagonal and off-diagonal disorder. It is shown that the average-state fidelity, typically employed in the literature for the quantification of the transfer, may overestimate considerably the performance of the protocol in a single realization, leading to faulty conclusions about the success of the transfer.