Quantum randomness from multi-pixel optical detection

随机数在科学、统计学、密码学、游戏和其他领域有许多用途。量子随机数发生器是一种经过验证的随机数发生器，本文中的随机性是指结果的不可预测性。Bellinequalityviolation、最小熵界和熵估计是证明随机性的三种方法。介绍了实现量子随机数发生器的各种方法，比较了它们的方案和挑战，讨论了双模输入可分离，两个探测器位于分束器输出端的双模认证，其中Fock态输入达到最大最优猜测概率。采用二项分布模型描述两种模式的结果，得到了猜测概率的置信区间，并通过空间变换引入了多像素认证.计算了联合像素检测数的猜测概率。高斯照明的最佳光束半径为探测器尺寸的0：56倍。在相同总光子数的情况下，分别采用高斯照明和均匀照明进行了多次实验，结果表明高斯照明对于构建RNG更方便、更经济;采用三星Galaxy S7手机的CMOS探测器进行了双模认证和多像素认证的实验。采用双模式认证和81200像素认证计算最优猜测概率和最小熵。最小熵估计与实验测量。81200像素可以达到约300 000位的最小熵，而CMOS上的1200万像素则会更大。

Random numbers have many uses in science, statistics, cryptography, gaming, and otherfields. Quantum random number generators are developed with certified randomness.Randomness in this thesis is characterized by the unpredictability of outcomes. Bellinequality violation, min-entropy bound, and entropy estimation are the three methods forrandomness certification. Different methods of implementing quantum random numbergenerators are introduced and compared with their scheme and challenges.Two-mode certification is discussed with separable two-mode input and two detectorsat the output of a beam splitter, where Fock state input achieves the maximum optimalguessing probability. The binomial distribution model is employed to describe the twomodeoutcomes and a guessing probability confidence interval is obtained.Multi-pixel certification is introduced with spatial transformation. The guessing probabilityfor joint pixel detection number is calculated. The optimum beam radius for aGaussian illumination is 0:56 times of the detector size. Multiple trials with the sametotal photon number are discussed with both Gaussian illumination and uniform illumination.A Gaussian illumination is more convenient and economic for building theRNG.A CMOS detector from a Samsung Galaxy S7 phone is used in the experiment toverify both two-mode certification and multi-pixel certification. The optimal guessingprobability and min-entropy are calculated with two-mode certification and 81200-pixelcertification. The min-entropy is estimated with experimental measurements. A minentropyof around 300 000 bits can be reached with 81200 pixels and it will be largerwith 12 million pixels on CMOS.