Quantum information

For the journal with this title, see Historical Social Research.
In quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a twolevel quantum system. However, unlike classical digital states (which are discrete), a twostate quantum system can actually be in a superposition of the two states at any given time.
Quantum information differs from classical information in several respects, among which we note the following:
 It cannot be read without the state becoming the measured value,
 An arbitrary state cannot be cloned,
 The state may be in a superposition of basis values.
However, despite this, the amount of information that can be retrieved in a single qubit is equal to one bit. It is in the processing of information (quantum computation) that the differentiation occurs.
The ability to manipulate quantum information enables us to perform tasks that would be unachievable in a classical context, such as unconditionally secure transmission of information. Quantum information processing is the most general field that is concerned with quantum information. There are certain tasks which classical computers cannot perform "efficiently" (that is, in polynomial time) according to any known algorithm. However, a quantum computer can compute the answer to some of these problems in polynomial time; one wellknown example of this is Shor's factoring algorithm. Other algorithms can speed up a task less dramatically—for example, Grover's search algorithm which gives a quadratic speedup over the best possible classical algorithm.
Quantum information, and changes in quantum information, can be quantitatively measured by using an analogue of Shannon entropy, called the von Neumann entropy. Given a statistical ensemble of quantum mechanical systems with the density matrix ρ, it is given by
Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and the conditional quantum entropy.
Contents
Quantum information theory
The theory of quantum information is a result of the effort to generalise classical information theory to the quantum world. Quantum information theory aims to answer the following question:
What happens if information is stored in a state of a quantum system?
One of the strengths of classical information theory is that physical representation of information can be disregarded: There is no need for an 'inkonpaper' information theory or a 'DVD information' theory. This is because it is always possible to efficiently transform information from one representation to another. However, this is not the case for quantum information: it is not possible, for example, to write down on paper the previously unknown information contained in the polarisation of a photon.
In general, quantum mechanics does not allow us to read out the state of a quantum system with arbitrary precision. The existence of Bell correlations between quantum systems cannot be converted into classical information. It is only possible to transform quantum information between quantum systems of sufficient information capacity. The information content of a message can, for this reason, be measured in terms of the minimum number n of twolevel systems which are needed to store the message: consists of n qubits. In its original theoretical sense, the term qubit is thus a measure for the amount of information. A twolevel quantum system can carry at most one qubit, in the same sense a classical binary digit can carry at most one classical bit.
As a consequence of the noisychannel coding theorem, noise limits the information content of an analog information carrier to be finite. It is very difficult to protect the remaining finite information content of analog information carriers against noise. The example of classical analog information shows that quantum information processing schemes must necessarily be tolerant against noise, otherwise there would not be a chance for them to be useful. It was a big breakthrough for the theory of quantum information, when quantum error correction codes and faulttolerant quantum computation schemes were discovered.
See also
 Quantum clock
 Quantum computing
 Quantum statistical mechanics
 POVM (positive operator value measure)
 Information theory
 Quantum gravity
Journals
Among the journals in this field are
 International Journal of Quantum Information
 Journal of Quantum Chemistry
 Applied Mathematics & Information Sciences
External links and references
 Lectures at the Institut Henri Poincaré (slides and videos)
 Quantum Information Theory at ETH Zurich
 Quantum Information Perimeter Institute for Theoretical Physics
 Center for Quantum Computation  The CQC, part of Cambridge University, is a group of researchers studying quantum information, and is a useful portal for those interested in this field.
 Quantum Information Group The quantum information research group at the University of Nottingham.
 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 0387357254)
 The International Conference on Quantum Information (ICQI)
 New Trends in Quantum Computation, Stony Brook, 2010
 Institute of Quantum Information Caltech
 Quantum Information Theory Imperial College
 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.
Quantum information science General Quantum computer • Qubit • Quantum information • Quantum programming • Timeline of quantum computingQuantum communication Quantum capacity • Quantum channel • Quantum cryptography (Quantum key distribution) • Quantum teleportation • Superdense coding • LOCC • Entanglement distillationQuantum algorithms Universal quantum simulator • Deutsch–Jozsa algorithm • Grover's search • quantum Fourier transform • Shor's factorization • Simon's Algorithm • Quantum phase estimation algorithm • Quantum annealingQuantum complexity theory Quantum computing models Decoherence prevention Quantum error correction • Stabilizer codes • EntanglementAssisted Quantum Error Correction • Quantum convolutional codesPhysical implementationsQuantum optics Ultracold atoms Spinbased Superconducting quantum computing Charge qubit • Flux qubit • Phase qubitCategories: Quantum information theory
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