The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities -- entanglement, non-locality and randomness -- relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: For systems in a given entangled state, how many nonlocal correlations in a sequence can we obtain by measuring them repeatedly? And from this generated sequence of non-local correlations, how many random numbers is it possible to certify? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from an entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.
Almost all pure entangled states enable unbounded nonlocality sharing
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学与技术研究院）；Physics Department and NanoLund, Lund University（隆德大学物理系与纳米实验室）
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。
Strategic Non-Shareability of Quantum Correlations
MED-X Institute, The First Affiliated Hospital of Xi’an Jiaotong University（西安交通大学第一附属医院 MED-X 研究所）；College of Physics, Xi’an Jiaotong University（西安交通大学物理学院）
Self-guided certification of nonlocality in quantum networks
Instituto Milenio de Investigación en Óptica, Universidad de Concepción（孔塞普西翁大学米列尼奥光学研究所）；Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Universidad de Concepción（孔塞普西翁大学物理与数学科学学院物理系）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科技大学光子科学研究所）
Traceable random numbers from a nonlocal quantum advantage
University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Oak Ridge National Laboratory（橡树岭国家实验室）；Joint Quantum Institute（联合量子研究所）；University of Maryland（马里兰大学）；Center for Quantum Information and Control, University of New Mexico（新墨西哥大学量子信息与控制中心）；University of California, Berkeley（加州大学伯克利分校）；Quside Technologies（Quside 科技公司）
