  One of the crucial differences between mathematical models of classical and
quantum mechanics is the use of the tensor product of the state spaces of
subsystems as the state space of the corresponding composite system. (To
describe an ensemble of classical composite systems one uses random variables
taking values in the Cartesian product of the state spaces of subsystems.) We
show that, nevertheless, it is possible to establish a natural correspondence
between the classical and quantum probabilistic descriptions of composite
systems. Quantum averages for composite systems (including entangled) can be
represented as averages with respect to classical random fields. It is
essentially what Albert Einstein was dreamed of. Quantum mechanics is
represented as classical statistical mechanics with infinite-dimensional phase
space. While the mathematical construction is completely rigorous, its physical
interpretation is a complicated problem (which will not be discussed in this
paper).
