E. Knill, R. Laflamme, H. Barnum, D. Dalvit, J. Dziarmaga,
J. Gubernatis, L. Gurvits, G. Ortiz, L. Viola and W. H. Zurek
29 July 2002
QUANTUM INFORMATION PROCESSING, SCIENCE OF - The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.
Kluwer Encyclopedia of Mathematics, Supplement III
Research of the last few decades has established that quantum information, or information based on quantum mechanics, has capabilities that exceed those of traditional ``classical'' information. For example, in communication, quantum information enables quantum cryptography [1,2], which is a method for communicating in secret. Secrecy is guaranteed because eavesdropping attempts necessarily disturb the exchanged quantum information without revealing the content of the communication. In computation, quantum information enables efficient simulation of quantum physics [3], a task for which general purpose, efficient, classical algorithms are not known to exist. Quantum information also leads to efficient algorithms for factoring of large numbers [4,5], which is believed to be difficult for classical computers. An efficient factoring algorithm would break the security of commonly used public key cryptographic codes used for authenticating and securing internet communications. A fourth application of quantum information improves the efficiency with which unstructured search problems can be solved [6]. Quantum unstructured search may make it possible to solve significantly larger instances of optimization problems such as the scheduling and traveling salesman problems.
As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developing new applications of quantum information and on physically realizing controllable quantum devices. The purpose of this primer is to provide an elementary introduction to quantum information processing (Sect. 2), and then to briefly explain how we hope to exploit the advantages of quantum information (Sect. 3). These two sections can be read independently. For reference, we have included a glossary (Sect. 4) of the main terms of quantum information.
When we use the word ``information'', we generally think of the things we can talk about, broadcast, write down, or otherwise record. Such records can exist in many forms, such as sound waves, electrical signals in a telephone wire, characters on paper, pit patterns on an optical disk, or magnetization on a computer hard disk. A crucial property of information is that it is ``fungible'': It can be represented in many different physical forms and easily converted from one form to another without changing its meaning. In this sense information exists independently of the devices used to represent it, but requires at least one physical representation to be useful.
We call the familiar information stored in today's computers ``classical'' or ``deterministic'' to distinguish it from quantum information. It is no accident that classical information is the basis of all human knowledge. Any information passing through our senses is best modeled by classical discrete or continuous information. Therefore, when considering any other kind of information, we need to provide a method for extracting classically meaningful information. We begin by recalling the basic ideas of classical information in a way that illustrates the general procedure for building an information processing theory.