State-independent contextuality with identical particles

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 qudit, 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.