Hiding and masking quantum information in complex and real quantum mechanics

Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all according no-hiding and no-masking theorems derived recently. Here we show that any set informationally complete states neither hidable nor maskable, thereby strengthening known before. Then, by virtue Hurwitz-Radon matrices (representations Clifford algebra), about real correlations, although minimum dimension composite Hilbert space required increases exponentially with original space. Moreover, a maximal maskable within theory has surprising connection maximally entangled states. These results offer valuable insight on potential limit hiding masking information, which are intrinsic interest number active research areas.