In the 70s, after a contentious between the Italian Government and th Royal Family (the Victor Emanuel III's desendents), the Savoy Family won that some properties, like Racconigi, must be handed back to the Savoy sisters, but the King's quote must be confiscated by the Government.
The jewels, I think, have been ceded to the Government, with many others properties (the Royal Palace of Milan) in the first years of the XX century, so, the royal jewels became a State property. I don't know if all the jewels were ceded to the State.