Quality means affirmation or negation. Quantity means universal or particular scope. Simple conversion preserves quality, but may change quantity where required.
“No human is a stone” — universal negative.
“No stone is a human” — also a universal negative.
“All humans are animals” — universal affirmative.
“Some animals are humans” — particular affirmative.
Thus conversion does not preserve every quantifier. It preserves truth and affirmative or negative quality.