基于量子相对熵的量子关联研究

Quantum correlation is one of the most hottest questions in the fields of quntum information in recent years. It is closely related to quantum compution, quantum information processing and many essential questions in quantum mechanics. Quantum entanglement is a kind of nonlocal quantum correlations that has been widely used in quantum information processing. Recent studies have found that quantum (non-classical) correlations can exist even in separable state, and quantum entanglement is just one form of quantum correlation. Quantum discord as the measure of non-classical correlations immediately have received much attension since proposed. However, it is very difficult to give the formulae in mathematics. Relative entropy of discord is defined to quantify the quantum correlation by the distance of relative entropy. Throughout this project, on the one hand, we will quantify the relative entropy of entanglement, quantum dissonance and relative entropy of discord defined by quantum relative entropy. On the other hand, we will discuss the monogamy property in terms of quantum correlation arround quantum relative entropy.

量子关联是近几年量子信息理论所讨论的热点问题之一，它与量子计算、量子信息处理以及量子力学中许多问题都有密切联系。量子纠缠是一种非局域的关联，最近研究结果发现，可分态中也可以存在非经典的关联，量子纠缠只是量子关联的一部分。量子失协作为量子体系中总的非经典关联的一种度量，一经提出立刻引起了广泛的关注，但是，量子失协的计算在数学上非常困难。相对熵失协是利用距离相对熵的方法对量子系统中的量子关联进行定义。本项目就是围绕由量子相对熵定义的相对熵失协、dissonance 以及相对熵纠缠度等量子关联进行量化并且研究量子关联的单配性问题。

量子关联与量子相干在量子力学的发展中具有重要的实践意义。量子纠缠是一种非局域的关联，它只是量子关联的一部分。相比于不同形式的量子关联，量子相干可以描述量子态更具一般意义的性质，并提供更为丰富和复杂的物理涵义。本项目取得了如下研究成果：首先对两量子比特Ux不变量子态的相对熵纠缠度进行了量化；其次计算了一类量子底特态的迹距离相干度量；最后利用纠缠纯态构造了一类完全可分的量子多体态，并给出了这类多体态的可分的纯态分解式。