alertness vs on the qui vive

alertness and on the qui vive both are nouns.

Word	Noun	Adjective	Verb	Adverb
alertness	Yes	No	No	No
on the qui vive	Yes	No	No	No

As nouns, alertness and on the qui vive are synonyms defined as:

Other synonyms of alertness include sharp-sightedness.

alertness (noun)	on the qui vive (noun)
lively attentiveness	lively attentiveness
the process of paying close and continuous attention
a state of readiness to respond