Quantum Information Types

⋆ Since the world (so far as we know) is quantum mechanical, “classical” information must be some sort of “quantum information.” • The precise sense in which this is so remains a subject of investigation at the present time. Despite (or because of?) an enormous number of publications on the subject, the community has not arrived at any consensus. ◦ E.g., the term “classical information” is widely used in the literature by authors who would be embarrassed if asked to actually define what they are talking about. ⋆ The purpose of these notes is to indicate a scheme based on types or species of quantum information which represents at least one way of seeing how quantum information theory is connected to classical information theory as developed by Shannon and his successors, and in what way new phenomena arise when quantum effects are taken into account. • These new phenomena, which have no (direct, at least) classical analogs, include: teleportation, dense coding, quantum cryptography, quantum error correction, and, of course, quantum computing.