量子力学本质上的不可预测性正好可以用来生成真正意义上的随机数。本论文描述的随机数生成器的随机性和安全性通过量子背景相关性得到验证，Kochen- Specker（KS）定理能够将利用量子力学生成的结果与利用经典力学生成的结果区分开来。此项工作用一个囚禁的171Yb+离子的三个内部能级生成随机数。论文中的实验利用KS不等式，更具体地，利用了Klyachko-Can-Binicioglu- Shumovsky（KCBS）不等式，它表现了量子力学当中测量结果对测量背景的依赖性，这样既保持了严格的随机性，同时也大大简化了实验要求，能够以较快的速度生成随机数。实验生成的随机数据明显破坏了经典力学当中的KCBS不等式，验证了其随机性。而不等式的破坏值还能够进一步为生成的随机数字符串提供随机性最小熵的下限。再者，囚禁离子技术的探测效率趋近于完美，由此彻底克服了一般量子光学实验中存在的探测漏洞，充分地保证了随机性。此项实验工作提供了一个实用性的快速、安全的随机数的生成器，会在很多实际应用中发挥重要作用。此项工作可以通过进一步延伸关闭相容性漏洞，这项扩展需要囚禁一个具有稳定的搁置态的137Ba+ 离子，而这两种离子的混合囚禁可以通过完美的同时测量使随机数生成器更加高效。为此，我们需要控制离子的外部运动态来实现一个完全摆脱漏洞的随机数生成器。本论文的成果还包括在实验中通过拉曼跃迁技术实现了离子-激光的相互作用，还拓展出离子外部运动态中的声子数态|n>的加减操作。借助绝热蓝边带跃迁技术的开发，对于0到10的任何一个声子数n，离子的声子数态得到了+1或-1平移，并在实验中观察到了非经典声子态的产生。
The intrinsic unpredictability of quantum mechanics can be used to generate genuine randomness. This dissertation demonstrates a random number generator certified by quantum contextuality, where Kochen-Specker(KS) theorem distinguishes the results of classical theories from those of quantum mechanics. In my work, three internal levels in a single trapped 171Yb+ ion are used to generate random numbers.We observe a violation of a KS inequality, in particular, the Klyachko-Can- Binicioglu-Shumovsky (KCBS) inequality which shows the measurement result in quantum mechanics rely on the context of the measurement. In this way, we not only guarantee the randomness strictly, but also lower the experimental requirement, thus the speed of random number generation can be reasonably fast. Generated experimental result obvious breaks the inequality and certifies its randomness. Furthermore, the violation value of the inequality provides the bounds for the minimum entropy in the generated string. It can be emphasized that this experiment closes the detection loophole due to the perfect detection fidelity, which secures the random number generation. This experiment provides a practical fast and secure random number generator which will play an important role in various applications.This work can be extended to close the compatibility loophole by trapping a 137Ba+ ion which has stable shelving states, and hybrid trapping of these two species of ions in the same trap will further improve the random number generation by implementing perfect sequential measurement. It requires the control of external motional state of the ion to achieve a loophole-free random number generator. This dissertation involves the result in developing ion-light interaction by Raman transition technique and extension of addition and substraction operations to external motional phonon state |n> of the ion. By the development of adiabatic blue sideband transition, we accomplish +1 and -1 shift to phonon number for any n from 0 to 10 and observe the production of non-classical state of phonon.
