Abstract
As is well known, every mixed or pure state of a bipartite quantum system is given by a statistical operator, which determines, in terms of its two reduced statistical operators, the subsystem states. Necessary and sufficient conditions for the existence of a composite-system state, and, separately, for the possibility of its being correlated or uncorrelated in terms of the range dimensions of the three mentioned statistical operators are derived. As a corollary, it is shown that it cannot happen that two of the mentioned dimensions are finite and the third is infinite.