  We identify and characterize all the local quantum channels that preserves
the set of classical states, i.e., does not create any quantum correlations. At
first we show that the quantum correlations cannot be created from without if
and only if the local quantum channel preserves the commutativity, i.e., the
images of any two commuting states also commute. And then we provide an
operational necessary and sufficient criterion for a known quantum channel to
preserve the commutativity as well as a single observable to witness an
arbitrary unknown commutativity-preserving channel. All the distance-based
measures for quantum correlations, e.g., the geometric measure, are
non-increasing while the quantum discord defined by von Neumann measurements
can be increasing or decreasing under local commutativity-preserving channels.
