Although liquid helium is kind of a partial BEC, isn't a BEC one of the best examples of a coherent state? Except for certain quantum phase liquids, superfluid

Although liquid helium is kind of a partial BEC, isn't a BEC one of the best examples of a coherent state? Except for certain quantum phase liquids, superfluid systems often exhibit long-range phase coherence. I'd actually be curious to know the quantum discord of a superfluid Fermi gas.