Quantum information differs strongly from classical information, epitomized by the bit, in many striking and unfamiliar ways. Among these are the following:
The unit of quantum information is the qubit. Unlike classical digital states (which are discrete), a qubit is continuous-valued, describable by a direction on the Bloch sphere. Despite being continuously valued in this way, a qubit is the smallest possible unit of quantum information. The reason for this indivisibility is due to the Heisenberg uncertainty principle: despite the qubit state being continuously-valued, it is impossible to measure the value precisely.
Despite the awkwardly-named no-teleportation theorem, qubits can be moved from one physical particle to another, by means of quantum teleportation. That is, qubits can be transported, independently of the underlying physical particle.
Although a single qubit can be transported from place to place (e.g. via quantum teleportation), it cannot be delivered to multiple recipients; this is the no-broadcast theorem, and is essentially implied by the no-cloning theorem.
Classical bits may be combined with and extracted from configurations of multiple qubits, through the use of quantum gates. That is, two or more qubits can be arranged in such a way as to convey classical bits. The simplest such configuration is the Bell state, which consists of two qubits and four classical bits (i.e. requires two qubits and four classical bits to fully describe).
Multiple qubits can be used to carry classical bits. Although n qubits can carry more than n classical bits of information, the greatest amount of classical information that can be retrieved is n. This is Holevo's theorem.
Quantum encryption allows unconditionally secure transmission of classical information, unlike classical encryption, which can always be broken in principle, if not in practice. (Note that certain subtle points are hotly debated).
Linear logic describes the logic of quantum information, in analogy to how classical logic works with classical bits. Linear logic is much like classical logic, except that Gentzen's rules for cloning are omitted. That is, entailment cannot be used to clone or delete logical premises, since qubits cannot be cloned or deleted.
The study of all of the above topics and differences comprises quantum information theory.
Quantum information theory
The theory of quantum information is a result of the effort to generalize classical information theory to the quantum world. Quantum information theory aims to investigate the following question:
How is information stored in a state of a quantum system?
As mentioned in the introduction, an arbitrary quantum state cannot be precisely converted in classical bits; this is the content of the no-teleportation theorem.
The information content of a message M can be measured in terms of the minimum number n of qubits needed to encode the message. Such a message M is encoded with nqubits and n2 classical bits that describe the relative arrangement of the n qubits. The qubit is the smallest possible unit of quantum information.
Qwiki - A quantum physics wiki devoted to providing technical resources for practicing quantum information scientists.
Quantiki - A wiki portal for quantum information with introductory tutorials.
Charles H. Bennett and Peter W. Shor, "Quantum Information Theory," IEEE Transactions on Information Theory, Vol 44, pp 2724–2742, Oct 1998
Institute for Quantum Computing - The Institute for Quantum Computing, based in Waterloo, ON Canada, is a research institute working in conjunction with the University of Waterloo and Perimeter Institute on the subject of Quantum Information.
Quantum information can be negative
Gregg Jaeger's book on Quantum Information(published by Springer, New York, 2007, ISBN 0-387-35725-4)
The International Conference on Quantum Information (ICQI)
New Trends in Quantum Computation, Stony Brook, 2010
Research Group on Mathematics and Quantum Information Madrid
Institute of Quantum Information Caltech
Quantum Information Theory Imperial College
Quantum Information University College London
Quantum Information Technology Toshiba Research
International Journal of Quantum Information World Scientific
Quantum Information Processing Springer
USC Center for Quantum Information Science & Technology
Center for Quantum Information and Control Theoretical and experimental groups from University of New Mexico and University of Arizona.
Mark M. Wilde, "From Classical to Quantum Shannon Theory", arXiv:1106.1445.
Group of Quantum Information Theory Kyungnam University in Korea