基于Bell测试的自验证量子随机数的关键问题研究

Uncertainty, as an intrinsic property of quantum physics, makes it possible to generate quantum random numbers; furthermore, quantum random numbers can be self-tested by using quantum non-local correlations even if the devices are not trusted. In this project, we will carry out loophole exclusions and performance improvement in two directions of self-testing random number generators based on Bell tests. In the aspect of loophole exclusions, firstly, faced with this case that the study of closing randomness loophole is based on two parties which does not satisfy applied needs, we explore the necessary and sufficient conditions for closing the randomness loophole of self-testing quantum random number generator based on multiple-parties Bell test in practical application scenarios; secondly, faced with this case that the critical detection efficiency required for closing detection loophole of is high which leads to more difficult for applications, we construct the new Bell test which is applied to self-testing random number generators to reduce the critical detection efficiency. In the aspect of performance improvement, faced with the inefficiency of self-testing quantum random number generator based on linear Bell tests, we construct a novel self-testing quantum random number generators based on star-sharped Bell tests. The research results of this project can provide new ideas for realizing safer and higher performance self-testing random number generators, and enrich the theory of quantum random numbers.

不确定性作为量子物理的内禀属性使得产生量子随机数成为可能；进一步，即使设备不可信，利用量子非局域关联可以得到验证的量子随机数。本课题以基于Bell测试的自验证量子随机数为研究对象，拟开展关闭漏洞和提升性能两个方向的研究。在关闭漏洞方面，其一，针对目前关闭其随机漏洞的研究都是基于两个参与方不能满足应用需求的情况，我们探究关闭基于多方Bell测试自验证量子随机数发生器的随机漏洞所需要满足的充要条件；其二，针对目前关闭其探测漏洞所需临界探测效率高增加实验难度的情况，构造用于自验证随机数发生器的新型Bell测试使得临界探测效率降低。在提升性能方面，针对目前自验证量子随机数效率低下的问题，设计基于星形Bell测试的自验证量子随机数发生器。其研究成果将为实现更安全且高性能的自验证随机数发生器提供新思路，且丰富量子随机数理论。

针对基于Bell测试的自验证随机数发生器面临漏洞威胁和性能低下等问题，本课题以基于Bell测试的自验证量子随机数发生器为对象展开研究，针对非对称的倾斜CHSH Bell测试自验证随机数发生器的随机漏洞问题，给出了弹性的全局测量依赖度量，并给出了关闭其随机漏洞的充要条件；针对多测量的PBC链式Bell测试自验证随机数发生器的随机漏洞问题，给出了分布式测量依赖度量，构造了关闭随机漏洞的含参PBC链式Bell不等式，用于生成安全的可验证随机数；针对自验证随机数发生器的探测效率问题，构造了关闭探测漏洞且随机数生成率高的自验证随机数发生器；针对多参与方的Svetlichny Bell测试自验证随机数发生器的时间一致漏洞问题，刻画了多方时间一致事件度量，构造了免疫时间一致漏洞的Svetlichny Bell测试自验证随机数发生器。研究成果丰富了可验证量子随机数发生器的安全理论，也为设计安全、高效的设备无关量子密码协议提供了理论参考。