The phrase "on the q t" means to do something secretly or discreetly. Its antonyms can be "openly," "publicly," or "frankly." For example, if someone asks you about a secret project you have been working on, and you want to be honest, you could say, "I've been working on it openly, and I'll share more information with you." Similarly, if you want to contradict a rumor that has been circulating in secret, you could say, "I want to share with everyone publicly that the rumor is not true." The opposite of "on the q t" invites honesty and transparency in communication.