Can system entropy really be lower that k ln2?

Question

Some time ago I asked whether a system entropy below k ln 2 has ever been measured. There were no answers. Also, I found nothing in google scholar.

I found a statement by DeWitt, who wrote that any system is either there or not. Thus, he argues, every system has at least an entropy k ln 2.

On the other hand, many argue that a system that is in its ground state, if the ground state is unique, has an entropy k ln 1 = 0, and thus has vanishing entropy.

So what is the lowest entropy of a system: k ln 2 or zero?

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See: B. DeWitt, Quantum field theory in curved space-time, Physics Reports 19, 295 (1975).