Quantum Resource Theories: General Structures and Fundamental Applications

量子力学描述亚原子世界的方式似乎违反我们的日常经验。 最近，研究人员发现了利用这些令人惊讶的功能用于信息处理技术的创新方法。 量子系统现在被理解为拥有某些资源，如纠缠，相干性和非定域性，这些资源可以应用于下一代设备。 本研究项目将研究量子资源的一般数学理论。 它旨在促进量子力学的非经典特征如何使用有利于实验实施的物理过程来测量和操纵的理解。 最终，该项目的结果将有助于为未来基于量子的技术奠定理论基础，其中包括加密，计算和通信设备。 在实现其成果，该项目将有助于通过支持多元化的学生队伍准备下一代科学家。本研究将从两个互补的角度研究量子资源理论。 首先，它将研究存在于许多不同类型的量子资源理论中的一般数学特征。 具体来说，它将确定和研究一个一般的数学特征，称为完全物理一致性，自然出现在资源理论与现实的实验实现强烈兼容。 此外，它将研究非凸理论中的结构属性和资源度量。 作为第二个研究重点，本项目将研究量子非定域性和广义量子测量的特定资源理论。 这些资源理论的严格框架将集中在其业务性质的发展。 此外，量子力学的两个基本特征，非定域性和测量不相容性，将统一为半量子非定域博弈的等价资源。 作为一个实际应用，将介绍一种新的方法来构建测量设备独立的维度证人。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Quantum mechanics describes the subatomic world in ways that seem counterintuitive to our everyday experience. Recently, researchers have discovered innovative ways to harness these surprising features for use in information processing technologies. Quantum systems are now understood as possessing certain resources such as entanglement, coherence, and nonlocality, which can be applied in next-generation devices. This research project will study the general mathematical theory of quantum resources. It seeks to advance the understanding of how non-classical features of quantum mechanics can be measured and manipulated using physical processes that are conducive for experimental implementation. Ultimately the results of this project will help lay the theoretical foundation for future quantum-based technologies, which include cryptographic, computational, and communication devices. In attaining its results, this project will help prepare the next generation of scientists by supporting a diverse student workforce. This research will study quantum resource theories from two complementary perspectives. First, it will investigate general mathematical features that are present in many different types of quantum resource theories. Specifically, it will identify and study a general mathematical feature, known as full physical consistency, that naturally arises in resource theories strongly compatible with realistic experimental implementations. In addition, it will investigate structural properties and resource measures in non-convex theories. As a second research thrust, this project will examine the specific resource theories of quantum nonlocality and generalized quantum measurements. Rigorous frameworks for these resource theories will be developed that focus on their operational natures. Furthermore, nonlocality and measurement incompatibility, two fundamental features of quantum mechanics, will be unified as equivalent resources in semi-quantum nonlocal games. As a practical application, a novel method for constructing measurement device-independent dimensionality witnesses will be introduced.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.