量子纠缠的判定和度量相关问题研究

With the rapid progress in quantum information science, it has become more and more clear that quantum entanglement plays important roles in the discussions about the foundation of quantum mechanics, quantum computation and information. Quantum entangled states have been the key resources in quantum information processing such as quantum teleportation, dense coding, quantum cryptography, and quantum error correction. Over the last two decades, many sufficient conditions for detection of bipartite entanglement have been found for discrete variables. However, many things are still unclear to us in multipartite entanglement and continuous-variable entanglement. .. This project will focus on two subjects. One is detecting and quantifying discrete-variable entanglement. Based on the local uncertainty relations, we will propose conditions to detect genuine multipartite entanglement, and lower bounds of some multipartite entanglement measures. Moreover, we will also present lower bounds for several entanglement measures by using the fidelities between the target quantum state and bipartite higher-dimensional maximally entangled states, and thus one can estimate entanglement measures by performing a single observable measurement in experiments... The other one is detecting and quantifying continuous-variable entanglement. We try to propose continuous-variable multimode entanglement conditions by using spin squeezing inequalities, which have been employed to detect discrete-variable entanglement. Furthermore, the index permutation theorem has been proposed to detect discrete variable multipartite entanglement, we will generalize the index permutation theorem to continuous variable systems in order to detect continuous-variable multimode entanglement... This project will help us deeply understand multipartite entanglement and its roles in quantum information processing.

量子纠缠在量子力学基础讨论、量子计算与量子信息等方面起到了重要的作用，是一些量子信息处理过程如量子隐形传态、密集编码、量子保密通讯及量子纠错等关键资源。近二十年来，关于两体离散变量纠缠研究已经取得了较大的进展。然而，在多体和连续变量纠缠等方面还有很多重要的问题没有解决。本课题包含两方面内容，其一是离散变量纠缠的判定与度量。利用局域不确定关系给出真正多体量子纠缠的判定条件，以及一些多体量子纠缠度量的下界；利用量子态与两体高维最大纠缠态的保真度来估计出各种量子纠缠度量的下界，提出实验上只需要测量一个力学量平均值就能给出多种纠缠度量下界的方案。其二是连续变量纠缠的判定与度量。尝试将自旋压缩等判定离散变量多体量子纠缠的方法用在连续变量系统中；推广判定离散变量多体量子纠缠的指标交换定理至连续变量系统中。本项目有利于深刻理解多体量子纠缠和它在量子信息处理中的作用。

量子纠缠在量子力学基础讨论、量子计算与量子信息等方面起到了重要的作用，它是一些量子信息处理过程如量子隐形传态、密集编码、量子保密通讯及量子纠错等关键资源。近二十年来，关于两体离散变量纠缠研究已经取得了较大的进展。然而，在多体和连续变量纠缠等方面还有很多重要的问题没有解决。..本课题完成了两方面内容，(1)离散变量纠缠的判定与度量。我们利用变形Hardy不等式来推导出N-1种不等式，这些不等式不仅是N-1种不同的纠缠方式的多体纠缠判定不等式，同时也是N-1种不同的非局域性形式的多体非局域性的判定不等式。我们利用目标量子态与某些参考量子纠缠纯态之间的保真度给出一些纠缠度量的下界，我们还提出了一套一般性的方法，用来给出各种真正多体纠缠和量子相干性可实验上测量的下界。此外，我们与中国科学技术大学量子信息实验上合作的这两篇实验文章中，我们实验验证了某些量子态的多体真正纠缠及多体真正非局域性能够被这几种不等式判定出来，但是用原始的Svetlichny不等式反而不能判定。(2)连续变量纠缠的判定与度量。我们提出了连续变量量子失谐充分必要条件，并且给出了该充分必要条件对应的量子电路，从而完全解决了连续变量量子失谐的判定问题。..本项目有利于深刻理解多体量子纠缠和它在量子信息处理中的作用。