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We theoretically study the decoherence and the dynamical decoupling controlof nitrogen-vacancy center electron spins in high-purity diamond, where thehyperfine interaction with $^{13}$C nuclear spins is the dominating decoherencemechanism. The decoherence is formulated as the entanglement between theelectron spin and the nuclear spins, which is induced by nuclear spin bathevolution conditioned on the electron spin state. The nuclear spin bathevolution is driven by elementary processes such as single spin precession andpairwise flip-flops. The importance of different elementary processes in thedecoherence depends on the strength of the external magnetic field.

Decoherence and dynamical decoupling control of nitrogen-vacancy center electron spins in nuclear spin baths