I recently attended a seminar where a professor of quantum cryptography told the audience that one quantum qubit can theoretically store "infinite information". I was very intrigued by this statement, and me being an absolute novice in this domain, do not have the means of verifying the validity of his statement. My questions are as follows:
- Can we really compute the distance $|x - y| < \epsilon$ using a quantum qubit? If so, can anyone throw light on how this is done?
- Also, if not, how far along are we in actually computing this quantity?
- Can we measure if quantum computers approximate this quantity better (or worse?) than classical computers?
Thanks a lot in advance!