基于超纠缠态的量子通信研究

This project will study the hyperentanglement-based quantum communication and related physical questions. We will investigate the faithful sharing of hyperentangled states between remote parties over noisy channels, which is the precondition for quantum communication. The hyperentanglement concentration and hyperentanglement purification, which are based on different noise hypothesis, will be studied for specific hyperentangled states, as well as other possible methods to establish the faithful hyperentangled channel. The discrimination of hyperentangled state is the key step to read the information. On one hand, we will study the distinguishing protocols for different types of hyperentangled states resorting to current technology. On the other hand, the general rules for discriminating high-dimension multi-particle hyperentangled states will be discussed in theory, including the distinguishability of hyperentangled states by the linear evolution. Based on the results of hyperentanglement sharing and discrimination, the hyperentanglement-based quantum communication will be investigated, such as quantum teleportation, remote state preparation, and controlled teleportation and so on. The study will focus on the application of non-maximal hyperentanglement in quantum communication, especially the affection of the degree of entanglement of the channel on the success probability and efficiency of quantum communication and the demands of the quantum channel to achieve a secure communication. By studying this project, some useful quantum information processing for hyperentanglement will be obtained, based on which we can build complete quantum communication schemes. We believe our achievements will contribute to the development of quantum communication.

本项目将研究基于超纠缠态的量子通信以及相关的物理问题。研究超纠缠态的远距离保真共享，针对不同形式的超纠缠态提出实用高效的超纠缠浓缩和超纠缠纯化方案，并讨论其它对抗信道噪声实现超纠缠态保真共享的可能途径；针对不同形式的超纠缠态提出在现有实验条件下可实现的区分方案，从理论上讨论高维多粒子超纠缠态区分的普遍规律及其线性区分极限；研究基于超纠缠态的量子通信方案，如量子离物传态、量子远程态制备、可控离物传态等，重点讨论非最大超纠缠态在量子通信中的应用，探讨纠缠度对方案成功率和效率的影响及实现安全通信对信道的要求。通过本项目的研究，争取得到一些针对不同超纠缠态的实用高效的量子信息处理方法并在此基础上构建完整的安全通信方案，为量子通信的实用化进程做出贡献。

本项目开展了基于超纠缠态的量子通信研究。在量子态远程制备方面，我们首先指出了同行文章中的不足，提出了一个最优的量子赤道态远程制备方案。随后我们首次讨论了可控远程态制备中控制者控制力的问题并给出了对任意D维量子态远程制备中控制者控制力的下限。其次在超纠缠态区分方面，我们首先提出了一个借助时间纠缠自由度辅助实现的N粒子极化GHZ态完备区分方案。随后我们开创性地提出了自辅助的超纠缠态区分方案，分别对极化路径超纠缠态和极化时间超纠缠态进行了详细讨论。我们的方案虽然仍需借助于非线性相互作用区分其中一个自由度的量子态，但是我们第二步的区分只需线性相互作用，利用已区分的第一个自由度辅助第二个自由度的测量，极大地简化了方案并提高了整体成功率。此外，我们提出了一个基于目前实验条件下可制备的两粒子三自由度超纠缠态的超密集编码方案，方案利用固定的辅助自由度将16个两自由度完备超纠缠态基矢分为12 组，将单光子的信息传输率提高到了3.58比特。我们还对两粒子超纠缠态在线性光学元件下的可区分性进行了讨论，得到了n自由度超纠缠态在k个确定辅助纠缠自由度下可区分性的普适结果。我们同时证明，若要完备区分两粒子n自由度超纠缠态，我们至少需要n个辅助的确定纠缠自由度。此外，我们还对基于超纠缠态的量子信息处理以及基于光量子态避错和容错的量子通信两大分支进行了综述研究。