Quantum coherence is a basic concept in quantum mechanics, representing one of the most fundamental characteristics that distinguishes quantum mechanics from classical physics. Quantum coherence is the basis for multi-particle interference and quantum entanglement. It is also the essential ingredient for various physical phenomena in quantum optics, quantum information, etc. In recent years, with the proposal of a quantum coherence measurement scheme based on a resource theory framework, quantum coherence as a quantum resource has been extensively investigated. This article reviews the resource theories of quantum coherence and introduces the important applications of quantum coherence in quantum computing, quantum information, and interdisciplinary fields, particularly in quantum thermodynamics and quantum biology. Quantum coherence and its applications are still being explored and developed. We hope this review can provide inspiration for relevant research.
Quantum coherence is a basic concept in quantum mechanics, representing one of the most fundamental characteristics that distinguishes quantum mechanics from classical physics. Quantum coherence is the basis for multi-particle interference and quantum entanglement. It is also the essential ingredient for various physical phenomena in quantum optics, quantum information, etc. In recent years, with the proposal of a quantum coherence measurement scheme based on a resource theory framework, quantum coherence as a quantum resource has been extensively investigated. This article reviews the resource theories of quantum coherence and introduces the important applications of quantum coherence in quantum computing, quantum information, and interdisciplinary fields, particularly in quantum thermodynamics and quantum biology. Quantum coherence and its applications are still being explored and developed. We hope this review can provide inspiration for relevant research.
Quantum coherence is not only a fundamental concept of quantum mechanics, but also an important physical resource for quantum information processing. Along with the formulation of the resource theoretic framework of quantum coherence, the quantification of coherence is still one of the recent research focuses. Quantum coherence is also very fragile, and the environmental noise usually induces a system to decohere. Hence it is also an important subject to make clear the dynamical behavior and to seek a flexible way of preserving quantum coherence of an open quantum system. Besides, there are many potential applications of quantum coherence in quantum many-body system, quantum thermodynamics, quantum biology and other related fields. We review in this paper the resource theoretic framework for quantifying coherence and the relevant quantum coherence measures defined within this framework which includes the relative entropy of coherence, the l1 norm of coherence, the entanglement-based measure of coherence, the convex roof measure of coherence, and the robustness of coherence. We also review the dynamical behaviors of quantum coherence for certain open quantum systems, the coherence generating and breaking power of typical quantum channels, and the freezing phenomenon of quantum coherence. Moreover, we exemplify applications of quantum coherence in Deutsch-Jozsa algorithm, Grover search algorithms, and the study of quantum phase transitions in multipartite systems. We hope that these results may provide not only an overview of the relevant field, but also an outlook of the future research direction of this exciting field.
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.
One of the fundamental features that separates quantum physics from classical physics is the idea of quantum superposition, also known as coherence. This thesis concentrates on understanding quantum coherence in the mathematical framework of resource theories, viewing it both as a resource to be harnessed and as a way to quantitatively characterise quantum states in contrast to classical states. We first examine the type of coherence resource theory which has emerged recently to cope with general settings where the physical nature of the medium encoding information is not crucial, such as computation. We identify the set of quantum processes in which coherence is neither created nor used, and use these to provide a physically motivated resource theory pictured in terms of interferometry. Using the same concepts, we then find connections between coherence and discord, a type of quantum correlation. In particular, we show how coherence can be used to generate discord, and explore basis-dependent discord as an intermediate quantity. The second part of the thesis applies the resource theory framework to quantify quantum macroscopicity, taken here to mean the extent to which coherence exists in a system on a macroscopic scale. We find the appropriate type of resource theory for this purpose, giving criteria for good measures of macroscopic coherence. We use these criteria to evaluate some previously proposed measures and highlight the role of the quantum Fisher information. Next, we build up measures based on the concept of macroscopic distinguishability and use them to show that macroscopic quantum states are fragile to noise induced by interaction with an environment. Finally, we apply measures based on the Fisher information to a range of experiments involving mechanical degrees of freedom, in order to compare their macroscopicity.
Abstract Entanglement is one of the key properties of the quantum mechanical systems that is fundamentally different from a classical system. Quantum entanglement plays an important role in the debate concerning the foundations of physics but also is an important resource in various quantum information processes. In this article, we introduce basic concepts on EPR correlations and quantum entanglement, and review established entanglement criteria, and show how to use these criteria in the generation of entanglement by considering coherence-induced entanglement and correlated spontaneous emission laser.
Quantum mechanics is one of the most significant scientific theories in modern physics, concerned with the behavior of matter and energy at the atomic and subatomic scales. By introducing concepts such as the quantization of energy, wave–particle duality, the uncertainty principle, quantum superposition, and quantum entanglement, this theory has fundamentally transformed humanity's understanding of the underlying structure of the universe. The importance of studying quantum mechanics lies not only in its ability to explain the fundamental phenomena of nature but also in its extensive contribution to the development of advanced technologies, including quantum computing, medical imaging, laser technology, secure communications, and nanotechnology. The objective of this article is to examine the fundamental principles of quantum mechanics and analyze their applications across various scientific and technological fields. This study employs a library-based research method with a descriptive–analytical approach. The required data were collected and analyzed through an extensive review of books, peer-reviewed scientific articles, and other authoritative sources in the field of quantum physics. The findings indicate that quantum mechanics, in addition to playing a fundamental role in understanding the subatomic world, constitutes one of the principal foundations for the advancement of modern technologies. Furthermore, the results suggest that the continued development of quantum technologies has the potential to exert profound impacts on scientific, industrial, and medical fields in the future. Consequently, quantum mechanics is not merely a fundamental physical theory but also a key driver of innovation and transformation in contemporary science and technology.
This book delves into the burgeoning field of quantum resource theories, a novel and vibrant area of research within quantum information science that seeks to unify diverse quantum phenomena under a single framework. By recognizing various attributes of physical systems as "resources," this approach offers a fresh perspective on quantum phenomena, transforming our understanding and application of concepts such as quantum entanglement, coherence, and more. With a focus on the pedagogical, the book aims to equip readers with the advanced mathematical tools and physical principles needed to navigate and contribute to this rapidly evolving field. It covers a wide range of topics, from the foundational aspects of quantum mechanics and quantum information to detailed explorations of specific resource theories, including entanglement, asymmetry, and thermodynamics. Through rigorous mathematical exposition and a unique axiomatic approach, the book provides deep insights into the operational and conceptual frameworks that underpin quantum resource theories, making it an invaluable resource for graduate students, early-career researchers, and anyone interested in the cutting-edge developments in quantum information science.