All local quantum states are mixtures of direct products

According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797 (1994)], {\it nonideal} measurements, rather than ideal ones, may be more sensitive to reveal nonlocal correlations between distant parts of composite quantum systems. The outcome statistics of joint nonideal measurements on local states should by definition admit local hidden variable models. We prove that the density operator of a local composite system must be convex mixture of the subsystems' density operators. This result depends essentially on a plausible consistency condition restricting the class of admissible local hidden variable models.