  We propose and study a universal approach for the reconstruction of quantum
states of many body systems from symmetry analysis. The concept of minimal
complete set of quantum correlation functions (MCSQCF) is introduced to
describe the state reconstruction. As an experimentally feasible physical
object, the MCSQCF is mathematically defined through the minimal complete
subspace of observables determined by the symmetry of quantum states under
consideration. An example with broken symmetry is analyzed in detail to
illustrate the idea.
