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We analyzed the rate at which quantum information encoded in zero-energy Majorana modes was lost in the presence of perturbations. We showed that information could survive for times that scale exponentially with the size of the chain both in the presence of quenching and time-dependent quadratic dephasing perturbations, even when the latter had spectral components above the system’s energy gap. The origin of the robust storage, namely the fact that a sudden quench affected in the same way both parity sectors of the original spectrum, was discussed, together with the memory performance at finite temperatures and in the presence of particle exchange with a bath.

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