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Quantum correlation can be created by a local operation from some initiallyclassical states. We prove that the necessary and sufficient condition for alocal trace-preserving channel to create quantum correlation is that it is nota commutativity-preserving channel. This condition is valid for arbitraryfinite dimension systems. We also derive the explicit form ofcommutativity-preserving channels. For a qubit, a commutativity-preservingchannel is either a completely decohering channel or a mixing channel. For athree-dimensional system (qutrit), a commutativity-preserving channel is eithera completely decohering channel or an isotropic channel.

Necessary and sufficient conditions for local creation of quantum correlation