开放系统多体量子关联及相关问题研究

Quantum correlation and the related problem is one of the most important research interest in the field of quantum information science in recent years, but studies focused on multipartite quantum correlations and its effects have seldom been reported so far. In this research project, based on the theory of von Neumann entropy and matrix theory and by virtue of the notions of conditional entropy, mutual information, as well as the relative entropy, Frobenius norm, Bures distance and trace distance, we study the issue related to the characterization and quantification of the tripartite and multipartite quantum correlations, its monogamy relation and quantum nonlocality from the perspectives of both quantum measurement and distance measures. Based on these measures, we further study dynamical behaviors of multipartite quantum correlations and its related effects for both the atomic and the spin-chain systems, and discuss possible schemes for controlling quantum correlations as well as its application in quantum protocols such as dense coding and remote state preparation. Meanwhile, we study the entropic uncertainty relation from the perspective of quantum correlations, and try to reveal how the choice of various observables and various estimates affect the sensitivity and the range of entanglement witnessed by this relation.

量子关联相关问题是近年量子信息研究的热点之一，目前针对多体量子关联及其相关效应的研究还相对较少。本项目将以von Neumann熵相关理论和矩阵理论为基础，借助条件熵和互信息以及相对熵、Frobenius范数、Bures矩阵和迹距离等概念，从量子测量和"距离"度量两个不同角度探索三体和多体量子关联的度量、monogamy关系和量子非定域性问题，并以此为基础，以腔场-原子系统和自旋链系统为具体对象，研究开放系统中的多体量子关联动力学行为及相关量子效应，探讨相应的量子关联调控方案及其在稠密编码、远程态制备等量子信息处理过程中的应用，同时从量子关联的角度研究基于熵理论的不确定性关系，以及它作为纠缠见证应用时观测量和测量方式等的选择对于纠缠见证范围和灵敏度问题的影响，为量子信息相关理论的发展提供基础。

量子关联不仅是量子力学基本理论关注的一个核心问题，同时也是重要的量子信息处理资源，对量子态关联属性的刻画、度量及在开放系统中的调控问题进行研究具有理论和现实意义。我们的研究内容主要围绕上述主题展开，三年来取得的主要进展有：(1)提出了基于迹距离的测量诱导非定域性刻画和度量方案，并证明了它在完全正定和保迹映射下的单调性；（2）从量子关联竞争机制角度研究了纠缠辅助的熵不确定关系，对其本质进行了诠释，给出了它在量子隐形传态和纠缠见证中的应用，给出了基于它的量子失谐上界和量子失谐在多体系统中共享的受限机理；（3）研究了开放系统量子关联度量函数的演化分解率，得到了对应量子态应具有的代数结构以及适用于qubit态的Pauli信道和qutrit态的Gell-Mann信道的克劳斯算子表示形式；（4）研究了系统-热库耦合时量子失谐的鲁棒性、量子失谐在演化过程中的“突然改变”奇异行为、环境非马尔科夫效应与量子失谐演化规律的定量联系。这些工作可以为明确量子态的关联属性、新奇效应及量子关联在典型量子信息处理任务中的应用提供理论基础，为分析环境非马尔科夫性在量子关联调控中的作用提供理论依据。