Is solid helium a quantum crystal?

It had been proposed that superfluidity could coexist with crystalline order in solid helium, thanks its quantum properties. If true, solid helium would have been be the first "supersolid". For some years, one thought that this paradoxical coexistence of order in real and momentum space - named "supersolidity" - had been observed by several groups in the world. But nowadays, we understand that supersolidity does not exist in these crystals, but instead the mobility of their dislocations is so high in the low temperature limit and if all impurities are suppressed, that it does not resist to shear in some directions. The discovery of this "giant plasticity" in helium crystals is not less interesting than supersolidity. Its careful analysis has led to fundamental progress in the knowledge of dislocation networks and dynamics, which are basic phenomena at the origin of the plasticity of materials. Now a question remains: in the end, what is really quantum in these crystals? I will try to give some answers to it.