熵不确定度关系与量子非定域性的理论及实验研究

熵不确定度关系与量子非定域性在量子秘钥分发、纠缠验证、量子精密测量等方面承担重要角色。熵不确定度关系的下界提供了测量任意非对易物理量的预测结果的精度，因此其研究具有重要的理论意义和实际应用价值。量子非定域性是量子信息学的核心，其研究将会促进人们更加深刻地理解量子力学的基本概念，并逐步完善量子力学基础问题的理论框架。本课题拟开展优化熵不确定度关系与量子非定域性的理论和实验研究：1.研究熵不确定度关系更加紧致的下界及其在量子信息处理中的应用。基于互信息、Holevo量等，提出推广型的不确定度关系式。2.探索具体物理系统熵不确定度的演化及其贝尔非定域性。3.研究贝尔不等式与量子导引不等式及其物理应用。4.基于全光系统，进行推广型熵不确定度关系和贝尔不等式的实验验证。此课题的研究将为量子体系下的量子精密测量、纠缠验证以及量子密钥分发等信息处理提供重要的理论依据和实验支撑。

The entropic uncertainty relations and quantum nonlocality play an important role in quantum key distribution, entanglement verification, and quantum precision measurement. The lower bounds of the uncertainty relations provide the accuracy of the prediction result of measuring any non-commuting observables, therefore its investigations are of very importance to theoretical significance and practical application value. Quantum nonlocality is a fundamental topic in quantum information theory, its investigation will deepen our understanding of the basic concepts of quantum mechanics, and also gradually advance the theoretical framework of the fundamental issues of quantum mechanics. This subject intends to carry out theoretical and experimental investigations on optimal entropic uncertainty relations and Bell nonlocality, which lie in: 1. We study the tighter lower bound for the entropic uncertainty relations and its application in quantum information processing. The more optimized uncertainty relations are derived based on mutual information and Holevo quantities. 2. We explore the evolution of the entropic uncertainty relations and Bell nonlocality for some realistic physical systems. 3. We explore the generalizations of Bell inequality and quantum steering inequality and their physical applications. 4. Experimental verifications of generalized entropic uncertainty relationship and Bell inequality based on all-optical system will be performed. The research on this subject will provide important theoretical basis and experimental support for quantum precision measurement, entanglement verification, and quantum key distribution in quantum systems.