Quantum State Reconstruction of Many Body System Based on Complete Set of Quantum Correlations Reduced by Symmetry

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.