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We consider the buildup and decay of two-spin entanglement through phaseinteractions in a finite environment of surrounding spins, as realized inquantum computing platforms based on arrays of atoms, molecules, or nitrogenvacancy centers. The non-Markovian dephasing caused by the spin environmentthrough Ising-type phase interactions can be solved exactly and compared to aneffective Markovian treatment based on collision models. In a first case studyon a dynamic lattice of randomly hopping spins, we find that non-Markovianityboosts the dephasing rate caused by nearest neighbour interactions with thesurroundings, degrading the maximum achievable entanglement. However, we alsodemonstrate that additional three-body interactions can mitigate thisdegradation, and that randomly timed reset operations performed on the two-spinsystem can help sustain a finite average amount of steady-state entanglement.In a second case study based on a model nuclear magnetic resonance system, weelucidate the role of bath correlations at finite temperature on non-Markoviandephasing. They speed up the dephasing at low temperatures while slowing itdown at high temperatures, compared to an uncorrelated bath, which is relatedto the number of thermally accessible spin configurations with and withoutinteractions.

Exact Entanglement Dynamics of Two Spins in Finite Baths