维数证明及其半定规划松弛的性质
Properties of dimension witnesses and their semi-definite programming relaxations
摘要：
在本文中，我们开发了一种研究半设备无关随机扩展协议的方法，该协议在[Li et al.，Phys. Rev. A $\mathbf{87}$，020302（R）（2013）]。这种方法允许下界，半定规划，随机数生成器的基础上维证人获得的随机性。我们还研究了使用这种方法的一些随机性扩展的鲁棒性。我们显示的作用，一个假设的痕迹的测量算子和一种方法来避免它。该方法也推广到系统的任意尺寸，并为更一般形式的维证人，比它的前一份文件。最后，我们介绍了一个降维的过程，它可以用来从一个现有的证据，以获得一个新的具有更高的可证明的随机性。所提出的方法可用于实验[Ahrens等人，物理修订版信函$\mathbf{112}$，140401（2014）]。
英文摘要：
In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with semi-definite programming, the randomness obtained from random number generators based on dimension witnesses. We also investigate the robustness of some randomness expanders using this method. We show the role of an assumption about the trace of the measurement operators and a way to avoid it. The method is also generalized to systems of arbitrary dimension, and for a more general form of dimension witnesses, than it the previous paper. Finally, we introduce a procedure of dimension witness reduction, which can be used to obtain from an existing witness a new one with higher amount of certifiable randomness. The presented methods finds an application for experiments [Ahrens et al., Phys. Rev. Lett. $\mathbf{112}$, 140401 (2014)].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
