Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here, we discuss the fate of these coherence times when the system is perturbed in two different ways. First, we consider the effects of a unitary coupling connecting the ends of the chain; when the coupling is weak and non-interacting, we observe stable long-lived harmonic oscillations between the strong zero modes. Second, and more interestingly, we consider the case when dynamics becomes dissipative. While in general dissipation induces decoherence and loss of information, here we show that particularly simple environments can actually enhance correlation times beyond those of the purely unitary case. This allows us to generalise the notion of strong zero modes to irreversible Markovian time-evolutions, thus defining conditions for {em dissipative strong zero maps}. Our results show how dissipation could, in principle, play a useful role in protocols for storing information in quantum devices.
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