I am a physicist, and minimum is correct. Quantum uncertainty is not an entropy measure. Importantly, the 'minimum uncertainty' is not just about the width of

I am a physicist, and minimum is correct. Quantum uncertainty is not an entropy measure. Importantly, the 'minimum uncertainty' is not just about the width of the wavefunction in position space---the uncertainty principle (roughly speaking) says that the variance in position space times the variance in momentum space has a lower bound. A gaussian saturates that bound.