  We introduce a quantity called the coherence of purification which can be a
measure of total quantumness for a single system. We prove that coherence of
purification is always more than the coherence of the system. For a pure state,
the coherence of purification is same as the relative entropy of coherence.
Furthermore, we show that the difference in the coherence of purification of a
quantum state before and after the dephasing can capture residual quantumness.
In addition, we show that the entanglement of purification that can be created
by incoherent operation between two subsystems is upper bounded by the
coherence of purification of the original system. We show that the coherence of
purification is a resource in quantum state discrimination process. In the
absence of coherence, entanglement and quantum correlations, the coherence of
purification may play an important role in quantum information processing
tasks.
