Abstract: Firstly, we gave characterization of the pure state in the PTsymmetric quantum theory based on the relationship between the PTinner product and the original inner product of PTsymmetric quantum system. Secondly, we gave the characterization of the mixed state in the PTsymmetric quantum system. Finally, we studied the evolution of state in PTsymmetric quantum system, and gave a necessary and sufficient condition for the unitary evolution.

Key words: PTframe, evolution, mixed state, PTsymmetry, pure state