Quantum Information - Wikipedia, The Free Encyclopedia

Quantum informationFrom Wikipedia, the free encyclopedia

In physics and computer science, quantum information is physical information that is held in the state of a

quantum system. Quantum information is the basic entity that is studied in the burgeoning field of quantum

information theory, and manipulated using the engineering techniques of quantum information processing.

Much like classical information can be processed with digital computers, transmitted from place to place,

manipulated with algorithms, and analyzed with the mathematics of computer science, so also analogous

concepts apply to quantum information.

Contents

1 Quantum information

2 Quantum information theory

3 Journals

4 See also

5 References

6 External links and references

Quantum information

Quantum information differs strongly from classical information, epitomized by the bit, in many striking

and unfamiliar ways. Among these are the following:

A 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.

A qubit cannot be converted into classical bits; that is, it cannot be "read". This is the no-teleportation

theorem.

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.

An arbitrary qubit can neither be copied, nor destroyed. This is the content of the no cloning theorem

and the no-deleting theorem.

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.

Quantum information - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Quantum_information

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Qubits can be changed, by applying linear transformations or quantum gates to them, to alter their

state.

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).

Quantum information can be moved about, in a quantum channel, analogous to the concept of a

classical communications channel. Quantum messages have a finite size, measured in qubits; quantum

channels have a finite channel capacity, measured in qubits per second.

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 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 , 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 (http://www.mi.ras.ru/~holevo/eindex.html) and the conditional

quantum entropy.

Quantum algorithms have a different computational complexity than classical algorithms. The most

famous example of this is Shor's factoring algorithm, which is not known to have a polynomial time

classical algorithm, but does have a polynomial time quantum algorithm. Other examples include

Grover's search algorithm, where the quantum algorithm gives a quadratic speed-up over the best

possible classical algorithm.

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 simplest description[1] of generalized quantum information is provided by dagger compact

categories, in much the same way that categorical logic and type theory provide the foundations for

computer science. This extends the Curry–Howard correspondence between proof theory and

computation to quantum domains.


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The general framework for the manipulation of quantum states is given by categorical quantum

mechanics.

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 n qubits and n2 classical bits that describe

the relative arrangement of the n qubits. The qubit is the smallest possible unit of quantum information.

Quantum information can be transmitted through quantum channels, which do have a finite capacity. This is

analogous to the classical case, where the noisy-channel coding theorem defines the maximum channel

capacity of a classical communications channel. An important breakthrough for the theory of quantum

information occurred when quantum error correction codes and fault-tolerant quantum computation schemes

were discovered.

Quantum information can be manipulated and processed using quantum logic gates, in rough analog to the

processing of classical information with digital circuits.

Journals

Among the journals publishing new results in this field are

International Journal of Quantum Information

International Journal of Quantum Chemistry

Applied Mathematics & Information Sciences

See also

Information theory

Interpretations of quantum mechanics

POVM (positive operator valued measure)

Quantum clock

Quantum computing

Quantum gravity

Quantum information science

Quantum statistical mechanics


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Qutrit

Typical subspace

References

^ Bob Coecke, "Quantum Picturalism", (2009) Contemporary Physics vol 51, pp59-83. (ArXiv 0908.1787

(http://arxiv.org/abs/0908.1787))

1.

External links and references

Lectures at the Institut Henri Poincaré (slides and videos) (http://www.quantware.ups-tlse.fr

/IHP2006/)

Quantum Information Theory at ETH Zurich (http://www.qit.ethz.ch/)

Quantum Information (http://www.perimeterinstitute.ca/research/research-areas/quantum-information

/more-quantum-information) Perimeter Institute for Theoretical Physics

Center for Quantum Computation (http://cam.qubit.org/) - 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 (http://www.nottingham.ac.uk/mathematics/research/groups

/mathematical-physics/quantum-information.aspx/) The quantum information research group at the

University of Nottingham.

Qwiki (http://qwiki.caltech.edu/) - A quantum physics wiki devoted to providing technical resources

for practicing quantum information scientists.

Quantiki (http://www.quantiki.org) - 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 (http://www.iqc.ca/) - The Institute for Quantum Computing, based

in Waterloo, ON Canada, is a research institute working in conjunction with the University of

Waterloo (http://www.uwaterloo.ca) and Perimeter Institute (http://www.perimeterinstitute.ca/) on the

subject of Quantum Information.

Quantum information can be negative (http://www.damtp.cam.ac.uk/user/jono/negative-

information.html)

Gregg Jaeger's book on Quantum Information (http://www.springer.com

/east/home?SGWID=5-102-22-173664707-0&changeHeader=true)(published by Springer, New York,

2007, ISBN 0-387-35725-4)

The International Conference on Quantum Information (ICQI) (http://osa.org/meetings

/topicalmeetings/icqi/default.aspx)

New Trends in Quantum Computation, Stony Brook, 2010 (http://insti.physics.sunysb.edu/itp/conf

/simons-qcomputation2/program.html)


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Research Group on Mathematics and Quantum Information (http://www.mathqi.es/) Madrid

Institute of Quantum Information (http://www.iqi.caltech.edu/) Caltech

Quantum Information Theory (http://www3.imperial.ac.uk/quantuminformation) Imperial College

Quantum Information (http://www.ucl.ac.uk/quantum) University College London

Quantum Information Technology (http://www.toshiba-europe.com/research/crl/qig/index.html)

Toshiba Research

International Journal of Quantum Information (http://www.worldscinet.com/ijqi/ijqi.shtml) World

Scientific

Quantum Information Processing (http://www.springer.com

/new+%26+forthcoming+titles+%28default%29/journal/11128) Springer

USC Center for Quantum Information Science & Technology (http://cqist.usc.edu/)

Center for Quantum Information and Control (http://www.cquic.org/) 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 (http://arxiv.org

/abs/1106.1445).

Group of Quantum Information Theory (http://qubit.kyungnam.ac.kr/) Kyungnam University in Korea

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Quantum Information - Wikipedia, The Free Encyclopedia