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In [[physics]] and [[computer science]], '''quantum information''' is [[physical information]] that is held in the [[quantum state|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 computer]]s, [[communications channel|transmitted]] from place to place, manipulated with [[algorithm]]s, and analyzed with the [[mathematics]] of computer science, so also analogous concepts apply to quantum information.
 
==Quantum information==
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 [[EPR paradox|impossible]] to [[quantum measurement|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.
 
* Qubits can be changed, by applying [[linear transformation]]s or [[quantum gate]]s 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 [[Claude Shannon|Shannon]] [[Information entropy|entropy]], called the [[John von Neumann|von Neumann]] [[Von Neumann entropy|entropy]]. Given a [[statistical ensemble]] of quantum mechanical systems with the [[density matrix]] <math>\rho</math>, it  is given by <math> S(\rho) = -\operatorname{Tr}(\rho \ln \rho). \, </math> Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as [http://www.mi.ras.ru/~holevo/eindex.html Holevo entropy] and  the [[conditional quantum entropy]].
 
* [[Quantum algorithm]]s have a different [[computational complexity]] than classical algorithms. The most famous example of this is [[Shor's algorithm|Shor's factoring algorithm]], which does not have a [[polynomial time]] classical algorithm, but does have a polynomial time quantum algorithm.  Other examples include [[Grover's algorithm|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 [[premise]]s, since qubits cannot be cloned or deleted.
 
* The simplest description<ref>Bob Coecke, "Quantum Picturalism", (2009) ''Contemporary Physics'' vol '''51''', pp59-83. ([http://arxiv.org/abs/0908.1787 ArXiv 0908.1787])</ref> of generalized quantum information is provided by [[dagger compact category|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.
 
* 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 [[Information theory|classical information theory]] to the quantum world. Quantum information theory aims to investigate the following question:
<blockquote>
How is information stored in a state of a quantum system?
</blockquote>
 
As mentioned in the introduction, an arbitrary quantum state cannot be preciely 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'' [[qubit]]s and ''n''<sup>2</sup> classical [[bit]]s 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 channel]]s, 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 gate]]s, in rough analog to the processing of classical information with digital circiuts.
 
==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]]
*[[Typical subspace]]
 
== References==
{{reflist}}
 
==External links and references==
{{More footnotes|date=November 2011}}
* [http://www.quantware.ups-tlse.fr/IHP2006/ Lectures at the Institut Henri Poincaré (slides and videos)]
* [http://www.qit.ethz.ch/ Quantum Information Theory at ETH Zurich]
* [http://www.perimeterinstitute.ca/research/research-areas/quantum-information/more-quantum-information Quantum Information] Perimeter Institute for Theoretical Physics
* [http://cam.qubit.org/ 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.
* [http://www.nottingham.ac.uk/mathematics/research/groups/mathematical-physics/quantum-information.aspx/ Quantum Information Group] The quantum information research group at the [[University of Nottingham]].
* [http://qwiki.caltech.edu/ Qwiki] - A quantum physics wiki devoted to providing technical resources for practicing quantum information scientists.
* [http://www.quantiki.org 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
* [http://www.iqc.ca/ Institute for Quantum Computing] - The Institute for Quantum Computing, based in Waterloo, ON Canada, is a research institute working in conjunction with the [http://www.uwaterloo.ca University of Waterloo] and [http://www.perimeterinstitute.ca/ Perimeter Institute] on the subject of Quantum Information.
* [http://www.damtp.cam.ac.uk/user/jono/negative-information.html Quantum information can be negative]
* [http://www.springer.com/east/home?SGWID=5-102-22-173664707-0&changeHeader=true  Gregg Jaeger's book on Quantum Information](published by Springer, New York, 2007, ISBN 0-387-35725-4)
* [http://osa.org/meetings/topicalmeetings/icqi/default.aspx The International Conference on Quantum Information (ICQI)]
*[http://insti.physics.sunysb.edu/itp/conf/simons-qcomputation2/program.html New Trends in Quantum Computation, Stony Brook, 2010]
*[http://www.iqi.caltech.edu/ Institute of Quantum Information] Caltech
*[http://www3.imperial.ac.uk/quantuminformation Quantum Information Theory] Imperial College
*[http://www.ucl.ac.uk/quantum Quantum Information] University College London
*[http://www.toshiba-europe.com/research/crl/qig/index.html Quantum Information Technology] Toshiba Research
*[http://www.worldscinet.com/ijqi/ijqi.shtml International Journal of Quantum Information] World Scientific
*[http://www.springer.com/new+%26+forthcoming+titles+%28default%29/journal/11128 Quantum Information Processing] Springer
*[http://cqist.usc.edu/ USC Center for Quantum Information Science & Technology]
*[http://www.cquic.org/ Center for Quantum Information and Control] Theoretical and experimental groups from University of New Mexico and University of Arizona.
* Mark M. Wilde, [http://arxiv.org/abs/1106.1445 "From Classical to Quantum Shannon Theory", arXiv:1106.1445].
*[http://qubit.kyungnam.ac.kr/ Group of Quantum Information Theory] Kyungnam University in Korea
{{Quantum computing}}
 
[[Category:Quantum information theory]]
 
[[it:Informazione quantistica]]

Revision as of 00:30, 19 February 2014

How To Appear For The Very Best Real Estate Residence

Many folks go blind when they are dealing with foreclosures. They would search for any remedy to stay away from it no matter what the repercussions are. The most obvious alternative that causes less harm on the home proprietor is almost certainly brief selling. If you want to realize how these implications will influence you, you initial need to know what a limited sale is.

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The Internet allows the new real estate trader to develop a crew and get 1st-hand understanding of the areas that they want to do investing in. For illustration enable's say that you stay in Los Angeles, but want to spend in a small group in Houston. Now you have two alternatives here. You can do with the attempted-and-correct approach. Question all around hold out for a response from somebody that could perhaps advocate an individual to you in Houston. Or you could go correct ahead log on the web and begin hunting for Suresh Babu Gaddam Topeka agents. In that specific area that you hunting to invest in.

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