I think the rarest words in your sentence are “information” and “sentence” yet you can drop both of those and figure out your meaning, especially if the sentence is part of a broader conversation.

“Rare words carry the most” basically conveys what you’re saying but just more vague. And I think that’s a really important distinction. Rare words reduce ambiguity and increase the specificity of your sentence, but they don’t necessarily carry the most meaning.