Quantum information

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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.

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 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). 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, 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

-\operatorname{Tr}(S \ln S).

Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as the conditional quantum entropy.

[edit] See also

[edit] 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
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