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 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 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 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 greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness- enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
Abstract Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence can be extracted and used for quantum technological applications. In this work, the progress of this research is reviewed, focusing in particular on recent experimental efforts. After a brief review of the underlying theory, the main platforms for realizing the experiments are discussed: linear optics, nuclear magnetic resonance, and superconducting systems. Experimental detection and quantification of coherence, experimental state conversion and coherence distillation, and experiments investigating the dynamics of quantum coherence are then considered. Experiments exploring the connections between coherence and uncertainty relations, path information, and coherence of operations and measurements are also reviewed. Experimental efforts on multipartite and multilevel coherence are also discussed.
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.