“All information is physical”, the slogan advocated over many years by Rolf Landauer of IBM, has recently led to some remarkable changes in the way we view communications, computing and cryptography. By employing quantum physics, several objectives that were thought impossible in a classical world have now proven to be possible. Quantum communications links, for example, become impossible to eavesdrop without detection. Quantum computers (were they to be realized) could turn some algorithms that are labelled “difficult” for a classical machine, no matter how powerful, into ones that become “simple”. The details of what constitutes “difficult” and what “easy” are the subject of mathematical complexity theory, but an example here will illustrate the point and the impact that quantum information processors will have on all of us. The security of many forms of encryption is predicated on the difficulty of factoring large numbers. Finding the factors of a 1024-digit number would take longer than the age of the universe on a computer designed according to the laws of classical physics, and yet can be done in the blink of an eye on a quantum computer were it to have a comparable clock speed. But only if we can build one, and that's the challenge! No one has yet realized a quantum register of the necessary size, or quantum gates with the prerequisite accuracy. Yet it is worth the chase, as a quantum computer with a modest-sized register could out-perform any classical machine.
“All information is physical”, the slogan advocated over many years by Rolf Landauer of IBM, has recently led to some remarkable changes in the way we view communications, computing and cryptography. By employing quantum physics, several objectives that were thought impossible in a classical world have now proven to be possible. Quantum communications links, for example, become impossible to eavesdrop without detection. Quantum computers (were they to be realized) could turn some algorithms that are labelled “difficult” for a classical machine, no matter how powerful, into ones that become “simple”. The details of what constitutes “difficult” and what “easy” are the subject of mathematical complexity theory, but an example here will illustrate the point and the impact that quantum information processors will have on all of us. The security of many forms of encryption is predicated on the difficulty of factoring large numbers. Finding the factors of a 1024-digit number would take longer than the age of the universe on a computer designed according to the laws of classical physics, and yet can be done in the blink of an eye on a quantum computer were it to have a comparable clock speed. But only if we can build one, and that's the challenge! No one has yet realized a quantum register of the necessary size, or quantum gates with the prerequisite accuracy. Yet it is worth the chase, as a quantum computer with a modest-sized register could out-perform any classical machine.
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.
Information is physical. Today’s information processing and communication are classical: they are based upon the laws of Newton’s and Maxwell’s classical physics. This assertion holds all the way, from commercial computers and networks, up to their most abstract models, e.g. Turing machines. Research in quantum information was born some twenty five years ago, with the encounter of two major scientific achievements of the 20th century, namely quantum physics and information sciences. A technological motivation for that is an extrapolation of Moore’s law which seems to indicate that the amount of matter needed for one bit will be reduced to one particle sometimes before year 2020. A deeper, scientific driving force of this interdisciplinary research is that of looking for the consequences of having computation and communication based directly upon the laws of quantum physics, i.e. our current ultimate knowledge of the world of elementary particles, as described by quantum mechanics. Breakthroughs in cryptography, communications, information theory and algorithmics have shown that this transplantation from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science and physics. The principles 388 and most striking results and hot topics of this promising way of encoding, processing and communicating information are briefly introduced in this chapter from a mostly computer science point of view, with detailed examples in algorithmics and in cryptography. At the end of the chapter, a short list of some significant articles, textbooks and reports on quantum information are suggested for further reading.
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.
Information and computation theory have undergone a spurt of new growth, and a renewal of their historic connection to basic physics, as they have expanded to treat the intact transmission and processing of quantum states, and the interaction of such 'quantum information' with traditional forms of information. We may wonder why this did not happen earlier, as quantum principles have long been accepted as fundamental to all of physics. Perhaps the founders of information and computation theory, such as Shannon, Turing and von Neumann, were too accustomed to thinking of information processing in macroscopic terms, not yet having before them the powerful examples of the genetic code and ever-shrinking microelectronics. Be that as it may, information until recently has largely been thought of in classical terms, with quantum mechanics playing a supporting role in the design of the equipment to process it, and setting limits on the rate at which it could be sent through certain channels. Now we know that a fully quantum theory of information and information processing offers, among other benefits, a brand of cryptography whose security rests on fundamental physics, and a reasonable hope of constructing quan- tum computers that could dramatically speed up the solution of certain mathematical problems. These benefits depend on distinc- tively quantum properties such as uncertainty, interference and entanglement. At a more fundamental level, it has become clear that an information theory based on quantum principles extends and completes classical information theory, just as complex numbers extend and complete the reals. Besides quantum generalizations of classical notions such as sources, channels and codes, the new theory includes two complementary, quantifiable kinds of information— classical information and quantum entanglement. Classical infor- mation can be copied at will, but can only be transmitted forward in time, to a receiver in the sender's forward light cone. Entanglement in contrast, cannot be copied, but can connect any two points in space-time. Conventional data processing operations destroy entanglement, but quantum operations can create it and use it for various purposes, such as speeding up certain classical computa- tions and assisting in the transmission of classical information or intact quantum states. Part of the new quantum information theory is the qualitative and quantitative study of entanglement, and its interactions with classical information. Any means, such as an optical fibre, of delivering quantum systems more or less intact from one place to another, may be viewed as a quantum channel. Unlike classical channels, which are well characterized by a single capacity, quantum channels have several distinct capacities, depending on what one is trying to use them for, and what auxiliary resources are brought into play. New effects involving quantum information continue to be discovered, not only in the traditional areas of computation, channel capacity, and cryptography, but in areas such as commu- nication complexity and game theory.
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.
Information is physical: the laws which govern its encoding, processing and communication are bound by those of its unavoidably physical embodiment. In today's informatics, information obeys the laws of Newton's and Maxwell's classical physics: this assertion holds all the way from commercial computers down to (up to?) their most abstract models, e.g. Turing machines and lambda-calculus. Today's computation and communication are classical. Research in quantum information processing and communication was born some twenty five 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 based upon 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 cryptography, communications, information theory, algorithmics and, more recently, in abstract computational models, programming languages and semantics frameworks, have shown that this transplantation 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.From a computer scientist's point of view, which is my point of view, I will explain the basics, survey the main achievements, and outline the current hot topics and major challenges of this promising and stimulating research. I will not assume any prior knowledge in quantum mechanics from the audience.