I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity.
I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity.
The development of quantum mechanics and quantum physics in general is one of the greatest intellectual achievements of the 20th century. Initially, quantum physicists focused on mathematically describing and understanding the laws of a micro-world, comprised of atoms, molecules and photons. Nuclei and sub-atomic particles were discovered, particle physics evolved, and complex quantum systems in chemistry and solid-state physics are now described in terms of quantum physics. Within a century, quantum physics became the framework, which allows us to describe and predict, albeit with probabilities, the behavior of the microscopic world as we know it. The powerful quantum framework led to revolutionary technical advances for a century, such as semiconductor technology and the entire electronics industry based on it, enabling computers and the information age. The development of lasers found applications in many areas of our current technologies; we use them for printers, storing and retrieving information using CDs, industrial welding, medical surgery, and for range finding and communication purposes. Medical imaging using MRI is now a routine instrument, as are precision measurements using tunneling and atomic force microscopes. Superconducting technologies are used for high magnetic fields and many more current technologies are based on and enabled by the laws of quantum physics. While the framework of quantum physics has thus proven to be extremely successful and powerful, throughout the last century there were many conceptual, and to some extent philosophical, discussions on our understanding of quantum physics. As early as the 1930s, Einstein and Schrödinger realized that quantum physics allows for some peculiar states, which Schrödinger called “entangled”, which have a non-local character and thus do find an easy interpretation in our classical world. It took a few more decades until John Bell conceived a way to quantify such states, which thus became amenable to measurements. Only in the eighties and nineties of the last century did the generation of entangled states, their characterization and their subsequent application become feasible and accessible in laboratories. Early on, Bell states were proposed for applications in quantum communication, employing protocols based on teleportation. Soon, entanglement was recognized to be useful also for sensing, for precision measurements and eventually for quantum information processing. Starting with the early concept of a trapped-ion quantum computer introduced by Ignacio Cirac and Peter Zoller in 1995, many other platforms were proposed for quantum information processing, based on superconducting quantum bits, photonic processes, engineered quantum dots and many more. The first decade of the 21st century saw an explosive development of quantum information physics, which is by now a mature field and increasingly focuses on applications. Worldwide efforts are ongoing to realize quantum networks for secure communication and to implement quantum computers. Enhanced sensing has been demonstrated using advanced quantum states, and quantum simulators have been developed, already tackling problems that are hard to compute with classical computers. While architectures for full-fledged quantum computers are already available, the realization of such computers still requires the routine implementation of error correction, which is not yet available, for full scalability. Currently, noisy intermediate-scale quantum (NISQ) processors are already used for computations and are even accessible via cloud services. Since about 2000, quantum technologies have been developed for many platforms with the aim to surpass the capablities of their classical counterparts. Many such devices now make use of entangled states, which are seen as the new resource for advanced quantum technologies. For this, describing, understanding and generally mastering the generation and manipulation of entanglement is a key element. Moreover, both hardware and software technologies have to be improved in order to better control quantum devices. Mastering quantum phenomena for communication, metrology, simulation and computation purposes is currently one of the hottest topics in science since the wide applicability of quantum technologies will revolutionize these fields. The development of advanced quantum technologies is thus seen worldwide as a strategic area for generating technical knowledge and industrial evolution. This special issue intends to showcase the breadth and impact of the ongoing research in advancing quantum technologies. We have invited a selection of renowned scientists to present their work, and we are confident that this issue will find a broad readership and attract much interest within the scientific community.
Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.
1124 NOTICES OF THE AMS VOLUME 45, NUMBER 9 I n the twentieth century, the quest for deeper understanding of the laws of nature has largely revolved around the development of two great theories: namely, general relativity and quantum mechanics. General relativity is, of course, Einstein’s theory according to which gravitation results from the curvature of space and time; the mathematical framework is that of Riemannian geometry. While previously spacetime was understood as a fixed arena, given ab initio, in which physics unfolds, in general relativity spacetime evolves dynamically, according to the Einstein equations. Part of the problem of physics, according to this theory, is to determine, given the initial conditions as input, how spacetime will develop in the future. The influence of general relativity in twentiethcentury mathematics has been clear enough. Learning that Riemannian geometry is so central in physics gave a big boost to its growth as a mathematical subject; it developed into one of the most fruitful branches of mathematics, with applications in many other areas. While in physics general relativity is used to understand the behavior of astronomical bodies and the universe as a whole, quantum mechanics is used primarily to understand atoms, molecules, and subatomic particles. Quantum theory has had a much more complex history than general relativity, and in some sense most of its influence on mathematics belongs to the twenty-first century. The quantum theory of particles—which is more commonly called nonrelativistic quantum mechanics—was put in its modern form by 1925 and has greatly influenced the development of functional analysis, and other areas. But the deeper part of quantum theory is the quantum theory of fields, which arises when one tries to combine quantum mechanics with special relativity (the precursor of general relativity, in which the speed of light is the same in every inertial frame but spacetime is still flat and given ab initio). This much more difficult theory, developed from the late 1920s to the present, encompasses most of what we know of the laws of physics, except gravity. In its seventy years there have been many milestones, ranging from the theory of “antimatter”, which emerged around 1930, to a more precise description of atoms, which quantum field theory provided by 1950, to the “standard model of particle physics” (governing the strong, weak, and electromagnetic interactions), which emerged by the early 1970s, to new predictions in our own time that one hopes to test in present and future accelerators. Quantum field theory is a very rich subject for mathematics as well as physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory despite important efforts in constructive field theory. So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are Edward Witten is professor of physics at the Institute for Advanced Study. His e-mail address is witten@ias.edu.
This exhaustive quality-research paper covers the field of emerging materials and their intrinsic properties and including how they can be used in the future in quantum technologies. The arrival of quantum mechanics is one of the most important scientific discoveries of the 20th century, with the promise of new computer generations, enhanced information transfer and precision measurement. However, the development of future quantum technology is highly dependent on the discovery of new materials that enable us to control quantum phenomena. This article carefully considers a range of advanced materials that have emerged recently, such as novel superconductors, topological insulators and graphene derivatives, to explore the unique quantum properties of these materials and how they can be exploited in quantum devices. By using advanced experimental techniques, including angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM), advanced instruments that allow us to probe electronic structures, spin textures and topological properties with atomic electron and spin resolution, the areas with most interesting quantum properties can be discovered, key for the development of quantum technologies. This paper details understanding of quantum coherence and decoherence mechanisms of the advanced materials. Quantum coherence is one of the most important properties for using the quantum features of materials for information processing. Through quantum states and entanglement, the quantum coherence can be manipulated and enhanced, which is also intertwined with the environment. Better understanding of quantum coherence and the mechanisms of decoherence can help to improve future generations of quantum technologies. The results reported here help to explain the mechanisms leading to design and performance of new materials for the quantum technology revolution. Studying advanced materials not only advance the understanding of quantum nature but will also power future quantum computing, quantum communication and quantum sensing devices. Current research can take advantage of all aspects of these new materials and advance the boundaries of science, engineering, computing, information exchange and sensing.
Quantum Information is the science that aims to use the unusual behavior of the microscopic world, governed by the laws of Quantum Mechanics, in order to improve the way in which we compute or communicate information. Though the first ideas in this direction come from the early 80’s, it is in the last decade when Quantum Information has suffered an spectacular development. It is impossible to resume in a paper like this one the importance and complexity of the field. Therefore, I will limit to briefly explain some of the initial ideas (considered classical by now), and to briefly suggest some of the modern lines of research. By the nature of this exposition, I have decided to avoid rigor and to concentrate more in ideas and intuitions. Anyhow, I have tried to provide with enough references, in such a way that an interested reader could find there proper theorems and proofs.