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。量子随机数生成器的开发具有证明的随机性。本文中的随机性是指结果的不可预测性。贝尔不等式法、最小熵界和熵估计是随机性验证的三种方法。介绍了量子随机数发生器的不同实现方法，比较了它们的实现方案和面临的挑战，讨论了在分束器输出可分离的双模输入和两个探测器的情况下的双模认证，其中Fock态输入获得了最大的最佳猜测概率。用二项分布模型描述这两个模型的结果，得到一个猜测概率置信度区间，并通过空间变换引入多像素认证。计算了联合像元检测数的猜测概率。非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，讨论了高斯照明和均匀照明下的多次实验。高斯照明更方便、更经济地构建RNG。实验中使用了三星Galaxy S7手机的CMOS探测器来验证双模认证和多像素认证。用双模认证和81200像素认证计算了最优猜测概率和最小熵。用实验测量的方法估算了最小熵。81200个像素可以达到30万比特的极小熵，而在CMOS1200万个像素的情况下，它会更大。

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.