Quantum physics is the cornerstone of contemporary science,and has led to a revolution in high-tech development. Its combination with information science has resulted in the interdisciplinary field of quantum information. It provides a new train of thought for overcoming the limits of computer chip size. Since 1987,our investigations on quantum open system theory,quantum ecoherence,and the fundamental problems of quantum physics have kept pace with the rapid development of quantum information science in the last decade. Starting with Huan-Wu Peng's important research on open quantum systems (the quantum damped harmonic oscillator) at the end of the 1970s,we will review the basic concepts and scientific importance of this field. At the same time,we will give a brief description of our series of studies on the theory of quantum open systems and its applications in quantum information.
Quantum physics is the cornerstone of contemporary science,and has led to a revolution in high-tech development. Its combination with information science has resulted in the interdisciplinary field of quantum information. It provides a new train of thought for overcoming the limits of computer chip size. Since 1987,our investigations on quantum open system theory,quantum ecoherence,and the fundamental problems of quantum physics have kept pace with the rapid development of quantum information science in the last decade. Starting with Huan-Wu Peng's important research on open quantum systems (the quantum damped harmonic oscillator) at the end of the 1970s,we will review the basic concepts and scientific importance of this field. At the same time,we will give a brief description of our series of studies on the theory of quantum open systems and its applications in quantum information.
In the first part of this thesis we extensively review the general theory of open quantum systems. We introduce new approaches to describe, in a hopefully more transparent way, some aspects which are usually misleading in a broad range of the literature. In addition, we revise new concepts and methods developed in recent years that complement the general theory mainly developed in the 1970s. In the second part, we focus our attention on the so-called Markovian processes which have been described in the previous part. We study the validity of typical equations used in simple systems such as harmonic oscillators, and propose and check different strategies to describe Markovian dynamics in more complicated interacting systems. Finally we propose a counter-intuitive situation where some level of noise can be actually useful for information tasks. In the third and last part, we approach the problem of the non-Markovian description of open quantum systems. To quantify how non-Markovian an open quantum system is we introduce a computable measure and apply it to some relevant situations. We also propose a way of probing the complexity of an environment by visualizing properties of a pair of qubits embedded in it. In addition, we develop a technique based on orthogonal polynomial theory to transform a wide range of environments into simple chains of particles which can be efficiently simulated with numerical techniques.
Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.
Quantum information science is a rapidly growing research area for that it provides new insights to the fundamentals of quantum mechanics and offers a platform for the architecture of novel quantum technologies. The successfulness and practicality of this important scientific field rely on the controllability of a quantum system subject to a realistic noisy environment. The environment always leads to unintended dynamics of the system, and thus destroys its coherence and limits its applications. It is therefore important to understand these decoherence mechanisms from first principles, in order to minimize, or even remove, its adverse effect on the quantum system. The study of this open quantum system problem is usually based on some effective paradigms, where the environment is assumed to be "large", such that it can affect the quantum system without any back action. However, due to the demand for a high precision in quantum computation, such an approximate framework becomes questionable. We provide a new theoretical approach to treat this type of open quantum system problem, including the correlated dynamics between the system and the environment, by using a diagrammatic technique in the same spirit as the Keldysh non-equilibrium Green's function. In this formalism, both the environment and the photonic control are quantized. The dynamics of the system can be evaluated accurately for a time scale of small decoherence, but arbitrary quantum control, relevant to the need for quantum technologies. This offers a way of precise quantum noise calculations. We find how fundamental quantum correlations between the quantum control and quantum environment can arise, and are missing in the existing Master equation approximations. On the other hand, the study of the environment not only provides a better understanding of the decoherence, it also allows applicable designs of quantum operations between different qubit systems. In particular, we engineer a new protocol to entangle two qubits at a distance by projection measurements of their environments, the resonance fluorescence photons. We find exceptional improvements on the probability of success and the rate of entanglement based on the multiphoton environment approach, in comparison with the existing single photon entanglement scheme
Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David
During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse sets of research communities. This interest has arisen due to fundamental problematics as to how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the following question: what are the ultimate limits for controlling open system dynamics? We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity —also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g. , formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.
The last century has been a period of extreme interest for scientific research, marked by the overcoming of the classical frontiers of scientific knowledge.Research oriented towards the infinitely small and infinitely big, in both cases beyondthe borders of the visible. Quantum physics has led to a new Copernican revolution,opening the way to new questions that have led to a new view of reality. At the sametime, new theories have developed, involving every field of science, philosophy and art, rediscovering the link between unity and totality and the importance of humanpotential. In a transdisciplinary approach we consider quantum field theory, new ideason the concepts of vacuum and entanglement, metaphysical aspects of quantum revolution and the introduction of different interpretative approaches on the “Whole”.