Coherence Power of Quantum Processes

量子系统可以以不同的物理状态同时存在。人们普遍认为，这种自然的基本属性，即量子相干或叠加，代表着从量子信息处理、量子计量学到量子生物学等各种领域的基本成分。该项目旨在开发一个强大而通用的科学框架，以评估和控制自然和人工量子过程的相干产生能力。这一点很重要，因为高效产生量子相干的能力是所有量子技术的核心，并基于前所未有的计算和通信能力支撑着它们产生巨大社会影响的潜力。因此，该项目旨在促进基础科学的进步，并将有助于促进潜在颠覆性量子技术应用的发展。该团队将引入数学手段，量化与物理过程相关的各种量子力学操作的相干产生能力。数学方法基于概率工具和完全正向图。可以直接进行实验测试的严谨结果将会得到。这种方法引入了一种关于优雅的几何结构的公式，包括全局和局部结构。该团队还将在几个方向上扩展这一概念和数学框架，包括开放量子系统和量子算法的研究。这个团队还将探索量子相干性与现代凝聚态物理学中一些基本和有趣的问题的联系，例如多体定域化。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum systems can exist simultaneously in different physical states. This fundamental property of nature, known as quantum coherence, or superposition, is widely believed to represent an essential ingredient in a variety of fields ranging from quantum information processing and quantum metrology to quantum biology. This project aims to develop a powerful and general scientific framework to assess and control the coherence generating power of quantum processes, both natural and artificial. This is important because the ability to efficiently generate quantum coherence lies at the very heart of all quantum technologies, and underpins their potential for huge societal impact based on unprecedented computational and communication power. This project thus aims to promote the progress of fundamental science, and it will help to foster the development of potentially disruptive quantum technological applications.This team will introduce mathematical measures to quantify the coherence generating power of various quantum mechanical operations associated with physical processes. The mathematical approach is based on probabilistic tools and completely positive maps. Rigorous results that are amenable to direct experimental tests will be derived. This approach introduces a formulation in terms of elegant geometrical structures, both global and local. This team will also extend this conceptual and mathematical framework in several directions including studies of open quantum systems and quantum algorithms. This team will also explore the connection of quantum coherence with some fundamental and fascinating problems in modern condensed matter physics e.g., many-body localization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.