开放系统中熵不确定度关系的研究及其应用

熵不确定度关系在量子测量、纠缠度量、数据压缩中承担着重要角色。由于量子系统不可避免的受到外界噪声环境的影响，产生量子退相干效应，因此在量子信息处理中考虑实际环境对熵不确定度关系的影响具有重要意义。本课题拟开展开放系统中熵不确定度关系及其应用的研究：1. 探索开放系统的熵不确定度关系演化规律。分别研究噪声环境对于单比特系统熵不确定度关系的影响，以及在量子存储支撑下熵不确定度关系的影响。2. 优化熵不确定度的调控。基于量子弱测量、局域操作等技术，探索熵不确定度关系的优化调控。3. 研究熵不确定度关系在远程态制备、纠缠验证、量子秘钥安全分析等量子信息处理中的应用。此课题的研究将进一步为开放系统的量子信息处理、信息提取及量子精密测量提供理论支持。

Entropy uncertainty relation (EUR) plays an important role in the field of quantum measurement, entanglement measurement, and data compression. Real quantum systems unavoidably suffer from noisy environments, which leads to quantum decoherence, thus it is important to consider the effect of practical environment on EUR during quantum information processing. This project will investigate EUR and its applications in open systems. First, we will explore the evolutions of EUR in various open systems. To be explicit, we will explore the influence of noisy environment on EUR in single-qubit systems and EUR in the presence of quantum memory. Second, we will optimize the steering of EUR via different technologies involving quantum weak measurement and local operations. Third, we will explore its technical applications in quantum information processing including remote state preparation, entanglement verification and quantum key security analysis. Our efforts could provide important theoretical support for quantum information processing, information extraction and quantum precise measurement under open systems.