Single system and ensemble interpretation of pure quantum states

Statistical properties of finite quantum ensembles are derived from postulates for just those predetermined and dispersion-free results of measurements on single systems represented mathematically by eigenvalues of certain operators. For each observable X of a single system and integer n greater than or equal to 1, an observable Xsub n of an ensemble of n systems is defined operationally by measuring X on each member of the ensemble and averaging the n results. The commutator [Xsub n, Ysub n] of operators representing averaged observables is shown to decrease inversely with n, so that observables averaged over large finite ensembles approximate commuting macroscopic ones. Similarly the composite state psi sup n of every large homogeneous ensemble of n identically prepared systems is nearly a simultaneous eigenstate of every averaged observable Xsub n with eigenvalue (psi,Xpsi). (Auth.)