设备无关类量子随机数研究

Randomness is a valuable resource for applications ranging from cryptography to numerical simulation of physical. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modeling of such processes, possibly controlled by the eavesdropper, limit the reliability of random number generators in ways that are difficult to control. The device independent random number generation protocols require two black boxes, which are used for the quantum state processing. Based on quantum entanglement, the device independent protocol does not require any assumption about the internal working of the device. Randomness of the measurement outcome can be estimated by the Bell inequality violation and min-entropy function. The semi-device independent protocol requires two black boxes, which are used for the state preparation and measurement respectively, which assumes that the dimension of the system can be certified. Comparing with the device independent protocol, the semi-device independent protocol has much easier physical realization and much higher generation efficiency. In this project, we research on quantum nonlocal estimation method, construct new type of device independent protocols, prove the equivalence property between different protocols, and analyze properties of the measurement outcomes.

真随机数在数值模拟和密码学等方面有着非常重要的应用，真随机数的产生应该是对任何人都是不可预测的，很难通过数学方法产生，现有的真随机数生成方案必须是基于不可预知的物理过程。但是随机数生成物理设备可能存在误差，甚至被窃听者所控制。而这些设备的非理想特性是不可控的，因此会降低生成随机数的可靠性。设备无关类协议不依赖于器件的可靠性，其量子态处理过程均可以认为是黑盒子。设备无关方案依赖于纠缠，不需要任何设备内部约束，通过Bell不等式的违反判定测量结果的随机性。而半设备无关方案依赖于单向态制备和态测量方案，需要限定设备维度，通过维度目击不等式的违反判定测量结果的随机性。相比较设备无关方案，半设备无关方案有着更简单的实验要求及更高的随机数生成效率。本项目研究量子非局域性度量方法，构造新型的设备无关和半设备无关随机数生成方案，证明不同方案之间的等价特性，并分析输出随机数的基本性质。

本项目对半设备无关量子随机数和全设备无关量子随机数分别开展了深入研究，给出基于Hardy佯谬、Cabello佯谬、CGLMP不等式、Braunstein-Caves不等式和CHSH不等式构造的一系列量子维度目击不等式，并设计了可实验验证的设备无关和半设备无关随机数方案。基于量子维度目击不等式的理论基础研究，本项目建立了设备无关和半设备无关的内在关联，给出了非局域性关联产生随机性的一系列基本性质，包括随机数生成效率、系统噪声鲁棒性等。在设备无关类量子随机数研究的基础上，本项目分别结合维度关联和量子纠缠给出了两类半设备无关量子密钥分配方案。本项目的研究成果深化了对设备无关量子信息的理解，为后续设备无关类量子密码的实验研究奠定了坚实的理论基础。