Model type identification of four-level quantum systems by projective measurement

Hamiltonian of finite-dimensional quantum closed systems can be classified by its degeneracy and corresponding parameter models for the systems can be given respectively. Based on this kind of classification, we explore the model type identification problem for four-level quantum closed systems when projective measurement is available. We show that to a certain context the model type identification problem can be reduced to a problem of spectrum analysis. However when only one kind of projective measurement is available, the model type of a four-level quantum closed system can not be completely discriminated just by spectrum analysis for most cases. Furthermore, we give an experimental design to the complete model type identification of a four-level quantum closed system with a special kind of Hamiltonian by spectrum analysis, when more than one kind of projective measurement is available.