  It is known that the global state of a composite quantum system can be
completely determined by specifying correlations between measurements performed
on subsystems only. Despite the fact that the quantum correlations thus suffice
to reconstruct the quantum state, we show, using a Bell inequality argument,
that they cannot be regarded as objective local properties of the composite
system in question. It is well known since the work of J.S. Bell, that one
cannot have locally preexistent values for all physical quantities, whether
they are deterministic or stochastic. The Bell inequality argument we present
here shows this is also impossible for correlations among subsystems of an
individual isolated composite system. Neither of them can be used to build up a
world consisting of some local realistic structure. As a corrolary to the
result we argue that entanglement cannot be considered ontologically robust.
The argument has an important advantage over others because it does not need
perfect correlations but only statistical correlations. It can therefore easily
be tested in currently feasible experiments using four particle entanglement.
