Quantum randomness extraction for various levels of characterization of the devices
Yun Zhi Law, Le Phuc Thinh, Jean-Daniel Bancal, Valerio Scarani
备注：
11pages, 3 figures. Section II is a concise review of works on randomness, structured around three classes of adversarial power and three levels of characterization of the devices. In Section V, we discuss some subtleties of randomness extraction when an ancilla is required (POVMs, pointer measurements)
The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called "device-independent" level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this "tomographic" level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (POVMs, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of "steering", in which Bob's device is fully characterized while Alice's is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.
Higher rates for semi-device-independent randomness expansion by recycling input randomness
King’s College London（伦敦国王学院）；University of York（约克大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Queen Mary University of London（伦敦大学玛丽女王学院）
Infinite Randomness Expansion and Amplification with a Constant Number of Devices
我们提出了一个设备无关的随机性扩展协议，只涉及一个常数数量的非信令量子设备，实现\emph{infinite expansion}：从统一的私有随机性的$m$位开始，该协议可以产生无限数量的认证随机性，即$\exp(-Ω(m^{1/3}))$ -接近均匀和安全的量子对手。依赖于输入大小的唯一参数是协议的可靠性和输出的安全性（在$m$中两者都是逆指数）。这解决了随机性扩展和设备独立性领域长期存在的问题。我们的协议的分析涉及克服\emph{adaptive}设备无关协议的研究中的基本挑战。我们的主要技术贡献是设计和分析的设备无关的协议是\emph{Input Secure}，也就是说，他们的输出是保证对量子窃听者，\emph{even if the input randomness was generated by that same eavesdropper}是安全的！输入安全性的概念可能对其他领域（例如与设备无关的量子密钥分发）具有独立的兴趣。
Experimental Test of Sequential Weak Measurements for Certified Quantum Randomness Extraction
量子非定域性提供了一种产生随机数的安全方法：它们的不可预测性是内在的，只需观察测量结果的统计数据就可以证明，而无需假设它们是如何产生的。为了做到这一点，纠缠对的产生和测量违反了贝尔不等式的结果统计。然而，经过一次投影量子测量后，纠缠被完全破坏，不能再使用。这一事实对采用投影测量时从每个量子态产生的随机数的数目提出了上限。相反，通过使用弱测量，可以保持和重新利用一些纠缠，并且弱测量序列可以从单个状态中提取无限数量的随机性，如Phys. Rev. A 95，020102（R）（2017）中所预测的那样。我们研究了这些弱测量的可行性，分析了它们应用于量子态中的缺陷的鲁棒性，然后使用基于偏振纠缠光子对的光学装置对其进行测试。我们表明，弱测量是可实现的，但只能在接近理想的条件下，才能提高随机生成的性能。
Stream randomness extraction against quantum side information
Future Research Lab, China Mobile Research Institute（中国移动研究院未来研究实验室）；Department of Physics, Renmin University of China（中国人民大学物理系）；QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong（香港大学计算机科学系量子信息与计算倡议）
Deterministic randomness extraction for quantum random number generation with partial trust
Quside Technologies S.L.（Quside科技有限公司）；Universitat de Barcelona（巴塞罗那大学）；ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究所）
Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
我们证明，正如Ac\'ın等人[Phys. Rev. A 93，040102（R）（2016）]所证明的那样，可以使用Gisin优雅的贝尔不等式的最大量子违反，以设备无关的方式从一位纠缠中证明两位随机性。这表明了一个令人惊讶的最大纠缠之间的联系，相互无偏基地的完整集合，对称信息完全的积极运营商值的措施，一方面，和最佳的方式证明最大的随机性，另一方面。
Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements
虽然最近已经证明了如何以设备无关的方式证明任何纯两量子比特纠缠态的最大随机性[E。Woodhead等人，Phys. Rev. Research 2，042028（R）（2020）]，来自更高局部维度的纠缠态的最佳随机性认证的问题仍然是开放的。在这里，我们介绍了一种方法的设备无关的认证的最大可能数量的$2\log_23$随机比特使用纯二分纠缠两quutrit状态和极端的九个结果一般非投影测量。为此，我们利用最近在[S. Sarkar等人，arXiv：2110.15176]，它结合了一种设备无关的方法来证明三维希尔伯特空间中的完全Weyl-Heisenberg基，以及一种单侧设备无关的方法来证明两个quitri部分纠缠态。
Semi-device-independent randomness certification on discretized continuous-variable platforms
Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；QuIIN - Quantum Industrial Innovation, EMBRAPII CIMATEC Competence Center in Quantum Technologies, SENAI CIMATEC（QuIIN量子工业创新，EMBRAPII CIMATEC量子技术能力中心，SENAI CIMATEC）；Center for Macroscopic Quantum States bigQ, Department of Physics, Technical University of Denmark（丹麦技术大学宏观量子态bigQ研究中心）
Lund University（隆德大学）；University of Jyväskylä（于韦斯屈莱大学）；Technical University of Denmark（丹麦技术大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
