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 two-state quantum system. However, unlike classical digital states (which are discrete), a two-state quantum system can actually be in a superposition of the two states at any given time. A simple introduction to this subject is provided in Basics of quantum mechanics. ... Physical information refers generally to the information that is contained in a physical system. ... Fig. ... To meet Wikipedias quality standards and make it more accessible, this article needs a better explanation of technical details or more context regarding applications or importance to make it more accessible to a general audience, or at least to technical readers outside this specialty. ... Quantum superposition is the application of superposition principle to quantum mechanics. ...

Quantum information differs from classical information in several respects, among which we note the following:

• It cannot generally be read or duplicated without disturbance (no cloning theorem).
• There can exist superpositions of different values; quantum information processing can be exponentially more efficient than classical algorithms, as one state can exist in superposition of all possible states at once.

However, despite this, the amount of information that can be both stored and retrieved in a single qubit is equal to one bit. It is in the processing of information (quantum computation) that a difference occurs. The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. ... In mathematics, a quantity that grows exponentially (or geometrically) is one that grows at a rate proportional to its size. ...

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), at least not with any known algorithm. However, a quantum computer can compute the answer to some of these problems in polynomial time; one well-known 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 polynomial speed-up over the best possible classical algorithm. Quantum information processing is concerned with what we can and cannot do with quantum information. ... An illustration of a modern personal computer. ... In computational complexity theory, Polynomial time refers to the computation time of a problem where the time, m(n), is no greater than a polynomial function of the problem size, n. ... Flowcharts are often used to represent algorithms. ... Shors algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, named after Peter Shor. ... Grovers algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N1/2) time and using O(logN) storage space (see big O notation). ...

Quantum information, and changes in quantum information, can be quantitatively measured by using an analogue of Shannon entropy. Given a statistical ensemble of quantum mechanical systems with the density matrix S, it is given by Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ... Entropy of a Bernoulli trial as a function of success probability. ... In physics, a statistical ensemble is a very large set of similar systems, considered all at once. ... A density matrix, or density operator, is used in quantum theory to describe the statistical state of a quantum system. ...

See also

• quantum statistical mechanics
• POVM (positive operator value measure)

Quantum statistical mechanics is the study of statistical ensembles of quantum mechanical systems. ... In functional analysis and quantum measurement theory, a POVM (Positive Operator Value Measure) is a measure whose values are non-negative self-adjoint operators on a Hilbert space. ...

External links and references

• 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.
• Qwiki - A quantum physics wiki devoted to providing technical resources for practicing quantum information scientists.
• 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 the Perimeter Institute on the subject of Quantum Information.
• Quantum information can be negative

• The Sabanci University School of Languages Podcasts: Quantum computation and quantum information by Zafer Gedik