Abstract: By using the definition and properties of the coherence measure, we studied the state ordering of the pure state and the mixed state respectively in a single quantum system, and gave the state ordering results between C_max,C_vmax and C_r,C_I,C_l1 The results show that C_r,C_Ι, and C_H provide the same state ordering for pure states, but this state ordering result is not formed for mixed states. Unlike entanglement measures, the order relationship between two coherence measures in a pure state may not necessarily have the same result for any state.

Key words: quantum coherence, coherence measure, state ordering