Jonathan D. Schultz, Jonathon L. Yuly, Eric A. Arsenault, Kelsey A. Parker, Sutirtha N. Chowdhury, Reshmi Dani, Sohang Kundu, Hanggai Nuomin, Zhendian Zhang, Jesús Valdiviezo, Peng Zhang, Kaydren Orcutt, Seogjoo Jang, Graham R. Fleming, Nancy Makri, Jennifer P. Ogilvie, Michael J. Therien, Michael R. Wasielewski, David N. Beratan
Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.
Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.
Quantum information, a field in which great advances have been made in the past decades, now presents opportunities for advanced chemistry. One roadblock to progress, especially for experimental chemical science, is that new concepts and technical definitions need to be learned. In this paper, we review some basic, but sometimes misunderstood, concepts of quantum information based on the mathematical formulation of quantum mechanics that will be useful for chemists interested in discovering ways that chemistry can contribute to the quantum information field. We cover topics including qubits and their density matrix formalism, quantum measurement as a quantum operation, information theory, and entanglement. We focus on the difference between the concepts in the quantum context and the classic context. We also discuss the relation and distinction among entanglement, correlation, and coherence. We aim to clarify the rigorous definition of these concepts and then indicate some examples in physical chemistry.
Quantum science underpins many of the most significant advances in modern physics, chemistry, and information technology. Quantum physics provides the fundamental laws governing matter and energy at microscopic scales, quantum chemistry applies these principles to explain molecular structure, bonding, and reactivity, and quantum computing seeks to exploit quantum phenomena such as superposition and entanglement to enable new computational paradigms. Despite their long-standing theoretical foundations and experimental successes, all three domains remain surrounded by persistent misconceptions, often amplified by abstract formalisms, popular science narratives, and rapid technological developments. This contemporary review critically examines the established facts and common myths associated with quantum physics, quantum chemistry, and quantum computing. Emphasis is placed on experimentally verified principles, computational feasibility, and realistic assessments of current capabilities. Recent advances reported between 2020 and 2025 are reviewed to highlight genuine progress in areas such as quantum simulations, molecular modeling, and noisy intermediate-scale quantum (NISQ) devices, while also addressing their practical limitations. By distinguishing validated achievements from speculative claims, this review provides a balanced, evidence-based perspective on modern quantum science. The article aims to clarify enduring misconceptions, promote conceptual clarity across disciplines, and outline realistic future directions for research and applications in quantum technologies.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
The concept of coherence has been applied in the quantum theory of radiation and matter as well as in classical optics. We review here the meaning of the term in each case and show how these apparently different uses of the word coherence can be understood in terms of a single concept involving interference (nonzero cross terms), minimum uncertainty, and cohering (uniform variance) of the wave packet that describes the system. Self-induced transparency, superradiance, and superconductivity are discussed as dramatic examples of coherence.
Coherence is a familiar concept in physics. It is the driving force behind wavelike phenomena such as the diffraction of light. Moreover, wave–particle duality implies that all quantum objects can exhibit coherence, and this quantum coherence is crucial to understanding the behaviour of a plethora of systems. In this paper, which is written at an undergraduate level, we shall briefly introduce what is meant by coherence in a well-known classical setting, before going on to describe its quantum version. We will show that coherence is important in describing the properties of solid-state nanosystems and especially quantum dots. Simple experiments that reveal the coherent nature of matter—and how this leads to some very powerful applications—will be described. Finally, we shall discuss the fragility of coherence and shall introduce a method for describing decoherence in open quantum systems.
This paper reviews the partial contents of our two manuscripts displayed on arXiv and the nine published papers in some journals, and offers some new expressions. These contents explore the interpretation or research of some concepts and quantum phenomena in quantum mechanics, including foundational or fundamental issues, which delve into deeper questions beneath the basic principles. In our research, we primarily focus on the absence of interaction, or restore the external field potential energy to the interaction energy and consider the related environment qualitatively. We offer a slightly more accessible explanation for several typical quantum phenomena explained using counterintuitive coherent superposition states, summarizing that the wave nature of a particle, i.e., coherent superposition, originates from the interaction of a particle with the environment. We try to propose adding a new postulate to the fundamental postulates or principles of quantum mechanics, which we call the zeroth postulate: any material particle is not free, meaning that the interaction between a particle with its environment cannot be zero. This provides a possible foundation for understanding the wave nature of microscopic particles in quantum mechanics, specifically the coherent superposition pure states. To put this into practice, we propose a new double-slit experiment, hoping that someone will conduct it and predicting that the experimental results will show interference patterns while also identifying which slit a particle has passed through, thus resolving the which-way dilemma. Additionally, we provide explanations for quantum measurements and conservation laws different from those in general books of quantum mechanics.