分布式量子随机

Randomness plays an important role in modern science and technology, where true randomness and privacy are two prerequisites. Usually only pseudo-randomness is produced in the classical world, whose value is determined by a hidden variable so that it is already implicitly known beforehand. In the framework of quantum mechanics, it is straightforward to generate true randomness by measuring a quantum state |0>+|1> in the basis of {|0>, |1>}. In this way the measurement outcome is completely unpredictable in advance. Privacy means that the random value keeps secret against the adversary which amounts to that the random variable is independent of the state of the adversary's system. However usually a quantum system is not isolated, but is correlated with other systems, some controlled by friends and others by the adversary.Then how to generate independent randomness among the inter-trusted parties while keeping private against the adversary is an interesting problem. Furthermore notice that quantum states are distributed by quantum channels and quantum operations are usually restricted to incoherent operations in reality. Therefore we initiate the study of distributed quantum randomness in this proposal, focusing on distilling distributed private randomness from multipartite states and sending private randomness through a quantum channel, both under general quantum operations and incoherent operations. The topic is of importance in quantum information theory and may play a significant role in the future quantum network.

随机在科技领域有重要应用，具有两个特性：随机性和私密性。基于经典物理产生的随机是伪随机，其值为某隐含变量事先决定。基于量子物理能产生真正的随机，如在标准基下测量量子态|0>+|1>,出现0或1的结果无法预知。私密性即随机与对手的任何状态变量没有关联。但是量子体系不是孤立存在的，而是与其他量子体系关联在一起，其中有些由朋友掌控，有些由对手掌控。因此如何利用多体量子态产生私密随机是一个有趣的问题。进一步注意到量子态通过量子信道分发，可实现的量子操作可能是受限的，一个典型限制是非相干操作。基于上述，本项目提出研究分布式量子随机，内容包括: 1.多体量子态的私密随机提取；2.量子信道传输私密随机模型；3.非相干操作下多体量子态的私密随机提取；4.非相干操作下量子信道传输私密随机模型。本项目的研究对量子信息论具有重要的理论意义，对将来的量子互联网有实际应用意义。

量子随机是量子信息论中的重要概念，在量子科学技术中有着重要应用。该项目支持下完成的研究工作包括：(1)量子态的私密随机提取：建立了多体量子态分布式私密随机提取的资源理论；引入了独立私密随机态的概念；发展了处理私密随机提取的工具；导出了多种情形下独立私密随机比特率可达的区域，其中之一对耦于Slepian-Wolf定理。(2)量子信道的私密随机传输：建立了量子信道传输私密随机的信道模型；导出了信道容量公式，给出了反向相干信息函数的物理解释，从而解决了量子信息论中一个多年开放问题。(3)私密泄露：研究了部分态泄露导致密钥或私密随机比特降低的问题，给出了多种情形下的可信密钥或私密随机比特损失的上界；联系了密钥与复原映射和非马尔可夫过程的关系。(4)纠缠优势：研究了是否任何纠缠态都能帮助提高特定的信道传输经典信息；在有记忆信道情况下给出了部分答案，在无记忆信道给出了例子表明单向不可提取的纠缠态能提高经典信息传输。