Present information technology is based on the laws of classical physics. However, advances in quantum physics have stimulated interest in its potential impact on such technology. This article is an introductory review of three aspects of quantum information processing, cryptography, computation, and teleportation. The author serves up hors d'oeuvres on the relevant parts of quantum physics and the sorts of quantum systems which might form the building blocks for quantum processors. Quantum cryptography utilizes states of individual quantum systems for the transfer of conventional classical bits of information. The impossibility of measuring quantum systems without disturbing them guarantees the detection of eavesdropping and hence secure information transfer is possible. In a sense, teleportation is the inverse of cryptography, using more robust classical bits to faithfully transfer a quantum state through a noisy environment. Quantum computation utilizes the evolving quantum state of a complex system, which consists of many interacting individuals. If such a machine could be built, it would be capable of solving some problems which are intractable on any conventional computer; he illustrates this with Shor's (see Proc. 35th IEEE Symposium on Foundations of Computer Science, p.124, 1994) quantum factoring algorithm. Details are given of the current experimental achievements, proposals, and prospects for the future and of the patents granted to date.
Present information technology is based on the laws of classical physics. However, advances in quantum physics have stimulated interest in its potential impact on such technology. This article is an introductory review of three aspects of quantum information processing, cryptography, computation, and teleportation. The author serves up hors d'oeuvres on the relevant parts of quantum physics and the sorts of quantum systems which might form the building blocks for quantum processors. Quantum cryptography utilizes states of individual quantum systems for the transfer of conventional classical bits of information. The impossibility of measuring quantum systems without disturbing them guarantees the detection of eavesdropping and hence secure information transfer is possible. In a sense, teleportation is the inverse of cryptography, using more robust classical bits to faithfully transfer a quantum state through a noisy environment. Quantum computation utilizes the evolving quantum state of a complex system, which consists of many interacting individuals. If such a machine could be built, it would be capable of solving some problems which are intractable on any conventional computer; he illustrates this with Shor's (see Proc. 35th IEEE Symposium on Foundations of Computer Science, p.124, 1994) quantum factoring algorithm. Details are given of the current experimental achievements, proposals, and prospects for the future and of the patents granted to date.
Quantum theory has found a new field of application in the realm of information and computation during recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some notable aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as examples of the impact of quanta on the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement made possible in information processing by a quantum computer. Finally the authors provide some examples of current experimental realizations for quantum computers and future prospects.
Summary form only given. Quantum mechanics offers the information scientist a new rich resource, which is only recently being tapped to allow for secure communication in the form of quantum cryptography, and for tremendous parallelism in quantum information processing and computing. I will describe developments and prospects for each. Quantum cryptography has already advanced beyond the research laboratory to become a realizable technology with proven secret key distribution for encryption. Quantum computing, although at an earlier stage of development has been recognized as a major new development in physics, enables us (if a quantum computer is realizable) to attack problems previously thought to be too complex for normal computation in a reasonable time. Examples of quantum algorithms involving this kind of advantage are Shor's for fast factorization (in itself a threat to secure communication) and Grover's for database searching. I will discuss the ways quantum mechanics allow such a speed-up, stressing how quantum entanglement is the key resource being exploited, and how quantum gates, networks, and the processors may be implemented in a realistically noisy environment. Simple demonstrators have already been built, and I will discuss prospects for future realization of large-scale processors.
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the Einstein, Podolsky and Rosen (EPR) experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory and, arguably, quantum from classical physics. Basic quantum information ideas are next outlined, including qubits and data compression, quantum gates, the `no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC. To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high- Q optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC). An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times. The review concludes with an outline of the main features of quantum information physics and avenues for future research.
Information is physical: the laws which govern its encoding, processing and communication are those of its unavoidable physical embodyment. In today's computing, information obeys the laws of Newton's and Maxwell's classical physics: this assertion holds all the way from commercial computers down to their most abstract models, e.g. Turing machines and lambda-calculi. Today's computation is classical.Research in quantum information processing and communication (QIPC) was born some twenty years ago, as a child of two major scientific achievements of the 20th century, namely quantum physics and information sciences. The driving force of this interdisciplinary research is that of looking for the consequences of having information encoding, computation and communication obey the laws of quantum physics, i.e. the ultimate knowledge that we have, today, of the foreign world of elementary particles, as described by quantum mechanics. Breakthroughs in algorithmics, cryptography, information theory and abstract computational models have shown that this rerooting of information from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science.The aim of this tutorial is to give a survey of the principles, main results and long term perspectives of current research in QIPC, from a computer science point of view. No prior knowledge in quantum mechanics is required to follow this tutorial. There will be two parts:1 - Computation, the quantum way: quantum bits and quantum operations; two major quantum algorithms: quadratic speedup for unordered database search (Grover's algorithm), exponential speedup for integer factoring (Shor's algorithm);2 - Communication, the quantum way, and longer term perspectives: quantum state teleportation; a quantum cryptographic protocol for secret key distribution. Hot topics in QIPC research, state of the art in physical implementation of quantum computers.
Introduction Any technology that functions at the quantum level must face the issues of measurement and control. We have good reasons to believe that quantum physics enables communication and computation tasks that are either impossible or intractable in a classical world [NC00]. The security of widely used classical cryptographic systems relies upon the difficulty of certain computational tasks, such as breaking large semi-prime numbers into their two prime factors in the case of RSA encryption. By contrast, quantum cryptography can be absolutely secure, and is already a commercial reality. At the same time, the prospect of a quantum computer vastly faster than any classical computer at certain tasks is driving an international research programme to implement quantum information processing. Shor's factoring algorithm would enable a quantum computer to find factors exponentially faster than any known algorithm for classical computers, making classical encryption insecure. In this chapter, we investigate how issues of measurement and control arise in this most challenging quantum technology of all, quantum computation. The subjects of information theory and computational theory at first sight appear to belong to mathematics rather than physics. For example, communication was thought to have been captured by Shannon's abstract theory of information [SW49, Sha49]. However, physics must impact on such fundamental concepts once we acknowledge the fact that information requires a physical medium to support it.
The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.Quantum information processing includes investigations in quantum information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control.The science of quantum information processing is a highly interdisciplinary field.In the context of mathematics it is stimulating research in pure mathematics (e.g.coding theory, *algebras, quantum topology) as well as requiring and providing many opportunities for applied mathematics.The science of quantum information processing emerged from the recognition that usable notions of information need to be physically implementable.In the 1960s and 1970s researchers such as R. Landauer, C. Bennett, C. Helstrom and A. Holevo realized that the laws of physics give rise to fundamental constraints on the ability to implement and manipulate information.Landauer repeatedly stated that "information is physical", providing impetus to the idea that it should be possible to found theories of information on the laws of physics.This is in contrast to the introspective approach which led to the basic definitions of computer science and information theory as formulated by A. Church, A. Turing, C. Shannon and others in the first half of the 20th century.Early work in studying the physical foundations of information focused on the effects of energy limitations and the need for dissipating heat in computation and communication.Beginning with S. Wiesner's work on applications of quantum mechanics to cryptography in the late 1960s, it was realized that there may be intrinsic advantages to using quantum physics in information processing.Quantum cryptography and quantum communication in general were soon established as interesting and non-trivial extensions of classical communication based on bits.That quantum mechanics may be used to improve the efficiency of algorithms was first realized when attempts at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated.In the 1980s, P. Benioff and R. Feynman introduced the idea of a quantum computer for efficiently implementing quantum physics simulations.Models of quantum computers were developed by D. Deutsch, leading to the formulation of artificial problems that could be solved more efficiently by quantum than by classical computers.The advantages of quantum computers became widely recognized when P.