  The problem of dipole-dipole decoherence of nuclear spins is considered for
strongly entangled spin cluster. Our results show that its dynamics can be
described as the decoherence due to interaction with a composite bath
consisting of fully correlated and uncorrelated parts. The correlated term
causes the slower decay of coherence at larger times. The decoherence rate
scales up as a square root of the number of spins giving the linear scaling of
the resulting error. Our theory is consistent with recent experiment reported
in decoherence of correlated spin clusters.
