Superposition, coherence, and $\cal PT$ -symmetry

In this paper, we investigate $\cal PT$-symmetric quantum mechanics in the view of superposition and coherence theory. The important connections between the theories are discussed. It is argued that $\cal PT$-symmetric quantum systems are endowed with some stationary superposition or superposition-free property. A physical interpretation of $\eta$-inner product is given, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems.