Security of device-independent cryptography

设备无关（DI）量子信息旨在建立协议的安全性，而无需对所使用设备的内部工作进行任何假设[1]。相反，DI协议直接将安全性建立在设备的输入-输出行为上，通过向它们提供输入并记录输出，建立一个违反Bell不等式的条件分布。可以使设备无关的两个重要任务是随机性扩展和密钥分配，Bell不等式违反证明设备的行为是量子力学的，并可用于量化随机性或密钥的数量。证明此类协议的安全性归结为找到原始随机性或密钥的条件最小熵的严格下界，条件是任何一个丢弃者可能具有的所有边信息。最近，一种称为熵累积定理（EAT）[2]的新技术已经开发出来，它将问题简化为对每一轮的von Neumann熵的估计。这减少了理论问题，以优化所有可能的窃听策略，以证明安全性。这仍然是一个困难的任务，因为冯诺依曼熵是非线性的，因此通常的启发式优化技术不能保证收敛（不像例如可以用线性或半定规划解决的问题）。因此，这些问题的放松版本通常被研究[3，4]，它们具有更好的计算特性，但可能以更宽松的边界为代价，并且必须适当地表征这种放松的有效性和紧密性。这个博士的首要目标是开发和评估这样的松弛，产生的界限是紧的和计算成本低廉的计算。该项目将包括理论工作在推导和评估界限，并计算工作在解决由此产生的优化问题。这个项目利用了项目B中开发的几种技能。该学生将在约克大学攻读博士学位。

Device-independent (DI) quantum information aims to establish security of a protocol withoutmaking any assumptions on the inner workings of the devices used [1] . Instead, DI protocolsbase security directly on the input-output behaviour of the devices by feeding them inputs andrecording the outputs, building up a conditional distribution which should violate a Bell inequality.Two important tasks that can be made device-independent are randomness expansion and keydistribution and the Bell inequality violation certifies that the devices are behaving quantummechanically, and can be used to quantify the amount of randomness or key.Proving the security of such protocols boils down to finding tight lower bounds on the conditionalmin entropy of the raw randomness, or key, conditioned on all side information anyeavesdropper may have. Recently, a novel technique called the entropy accumulation theorem(EAT) [2] has been developed, which reduces the problem to an estimation of the von Neumannentropy of each round. This reduces the theoretical problem to the optimisation of this entropyover all possible eavesdropping strategies to prove security. This is still a difficult task, since thevon Neumann entropy is non-linear, and hence usual heuristic optimization techniques are notguaranteed to converge (unlike for instance problems that can be solved with a linear orsemidefinite program). Consequently, relaxed versions of these problems are typically studied[3,4] which have better computational properties at the possible expense of a looser bound, andthe validity and tightness of such relaxations must be properly characterised. The overarchinggoal of this PhD is to develop and evaluate such relaxations, producing bounds that are tightand computationally cheap to calculate.The project will consist of theoretical work in deriving and evaluating bounds, and computationalworking in solving the resulting optimisation problems. This project utilises several of the skillsdeveloped in project B. The student will conduct this PhD at the University of York.