Quantum resource theories

在过去的三十年里，量子信息理论的出现导致了对量子效应（如叠加和纠缠）的重要重新评估：从缺乏理解甚至矛盾的概念，这些现在被认为是实现经典物理学领域内不可能完成的任务的基本要素，从而实现了丰富的创新技术。这场革命的核心在于物质资源等现象的形式化和特征化。这种应用驱动的观点始于量子纠缠，并成功地应用于热力学中的纯度、相干性和信息不平衡等领域，激发了资源理论的形成，即以数学严谨的方式捕捉物理特征的资源特征的定量理论。资源理论的一般研究表明，所有不属于“自由”态凸子集的量子态都可以被视为资源，因为它们在操作任务（如信道识别）中提供了可量化的优势。本项目旨在更广泛地推进当前量子现象和物理资源理论的前沿知识。特别是，可能的方向包括：-发展动态资源理论的基础和应用，其中操作而不是量子态被仔细检查其在信息技术任务中的有用性，并研究多个竞争资源的理论。-根据实际的实验环境（例如，在传感和成像仪器中）调整资源理论，并确定在能量限制、组件的实际成本或外部噪声影响等物理限制下可实现的优势。-应用资源理论的结果，得出物理过程的基本限制的结论，例如表征从宏观到纳米和量子尺度的热力学结构，以及广义概率理论中智能的最终限制。

The emergence of quantum information theory in the last three decades has led to a crucial reassessment of quantum effects such as superposition and entanglement: from poorly understood and even paradoxical concepts, these are now regarded as fundamental ingredients to achieve tasks otherwise impossible within the realm of classical physics, thus enabling a wealth of innovative technologies. At the core of this revolution lies the formalisation and characterisation of such phenomena as physical resources. Initiated with quantum entanglement, and successfully applied e.g. to purity, coherence, and informational nonequilibrium in thermodynamics, this application-driven viewpoint motivates the formulation of resource theories, that is, quantitative theories capturing the resource character of physical traits in a mathematically rigorous fashion. General studies on resource theories have shown that all quantum states which do not belong to a convex subset of "free" states can be regarded as resources, in the sense that they provide a quantifiable advantage in operational tasks such as channel discrimination.This project aims to advance the current frontiers of knowledge on resource theories for quantum phenomena and physics more broadly. In particular, possible directions include:- Develop foundations and applications of dynamical resource theories, where the operations rather than the quantum states are scrutinised for their usefulness in information technology tasks, and investigate theories of multiple competing resources.- Tailor resource theories to realistic experimental settings (e.g. in sensing and imaging instruments) and determine the achievable advantage under physical constraints imposed by energy limitations, actual cost of components or external noise influences.- Apply results from resource theories to draw conclusions on fundamental limitations of physical processes, e.g. to characterise the structure of thermodynamics from macro- to nano- and quantum scale, and the ultimate limits of intelligence in generalised probabilistic theories.