The ensemble of prepared systems, in a definite pure state, then consists of a set of individual systems, all having one and the same definite energy, but each having a different quantum mechanical phase, regarded as probabilistically random. The wave function, however, does have a definite phase, and thus specification by a wave function is more detailed than specification by state as prepared.
The ensemble of prepared systems, in their pure state, consists of individual systems with identical energy and differing quantum mechanical phases, which are probabilistically random. The wave function has a definite phase, providing a more detailed description than simply stating the system's state as prepared.