It has been recently conjectured that the state-independency of quantum
contextuality may be lost when the indistinguishability of identical particles
is taken into account. Here, we show that quantum state-independent
contextuality exists for any system of more than one identical bosonic qudits,
and for most systems of fermionic qudits. The only exception is the case of d
fermionic qudits, since there the dimension of the antisymmetric subspace is 1,
which is insufficient for contextuality. For all the other cases, either the
symmetry precludes the existence of physical states, or we provide an explicit
method to produce quantum state-independent contextual correlations.Comment: REVTeX4, 5 page