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It has been found that Markovian quantum dissipative processes, described bythe Lindblad equation, may have attractive steady-state manifolds, in whichdissipation and decoherence can play a positive role to quantum informationprocessing. In this article, we show that such attractive steady-statemanifolds with the same positive features as in Markovian dissipative processescan exist in the non-Markovian dissipative processes. Our finding indicatesthat the dissipation-assisted schemes implemented in the Markovian systems canbe directly generalized to the non-Markovian systems.

Non-Markovian quantum dissipative processes with the same positive features as Markovian dissipative processes