Theoretical study of multi-layered CuO 2 surfaces with localization potential shows that (i) special stable macroscopic quantum states appear when [Formula: see text], where χ is the doping level and G is the unit-cell number, and that (ii) the physical phenomena related to ‖c charge motion takes place just as expected in the fictitious situation where whole uniformly doped holes concentrate in one-side surface. In the dielectric measurement of doping-level dependence and film-thickness dependence on c-oriented La 2-χ Sr χ CuO 4-δ film, we find that (a) anomalous low-frequency polarization is enhanced when a scaling parameter χG is near to [Formula: see text], that (b) quasi-static measurement of the polarization property in low doped film shows two typical characteristics explicable by the fictitious charge concentrations, and that (c) ‖c small-voltage conduction measurement on low doped film also shows two types of characteristic which are switched each other triggered by laser irradiation. Since these macroscopic quantum effects with plural levels with very long life time are observable even up to room temperatures, they may be useful in quantum computing application.