Quantum randomness from multi-pixel optical detection

随机数在科学、统计学、密码学、游戏和其他领域有很多用途。量子随机数发生器是基于证明随机性的。本文中的随机性以结果的不可预测性为特征。bell不等式违反、最小熵界和熵估计是三种验证随机性的方法。介绍了量子随机数生成器的不同实现方法，并比较了它们的方案和面临的挑战。讨论了在分束器输出可分离双模输入和两个检测器的情况下，Fock态输入达到最大最优猜测概率的双模认证。采用二项分布模型对两模态结果进行描述，得到一个猜测概率置信区间。采用空间变换引入多像素认证。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。讨论了高斯光照和均匀光照下总光子数相同的多次试验。高斯照明对于建立theRNG更为方便和经济。实验中使用了三星Galaxy S7手机的CMOS探测器来验证双模式认证和多像素认证。采用双模式认证和81200像素认证计算了最优猜测概率和最小熵。用实验测量估计了最小熵。使用81200像素可以达到约30万比特的最小熵，而在CMOS上使用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.