  Quantum correlation can be created by a local operation from some initially
classical states. We prove that the necessary and sufficient condition for a
local trace-preserving channel to create quantum correlation is that it is not
a commutativity-preserving channel. This condition is valid for arbitrary
finite dimension systems. We also derive the explicit form of
commutativity-preserving channels. For a qubit, a commutativity-preserving
channel is either a completely decohering channel or a mixing channel. For a
three-dimensional system (qutrit), a commutativity-preserving channel is either
a completely decohering channel or an isotropic channel.
