Extremal quantum correlations and cryptographic security

量子密码学是量子信息科学的一个成熟领域，量子通信的密码安全性已经被证明适用于许多不同的协议。尽管如此，防止窃听的基本安全结构还没有得到充分的研究。在最近的一篇论文中，我们确定了一个几何特征，即量子概率分布的极值，作为设备独立安全的充分必要条件。这是最强的安全性，不依赖于对物理设备正常运行的假设。在所提出的研究中，我们希望开发新的方法来研究和证明安全的概率分布。我们还将研究近似极值相关性，旨在表明这些仍然可以用于生成具有正速率的安全密钥。

Quantum cryptography is an established field of quantum information science and cryptographic security of quantum communication has been shown for a number of different protocols. Still, the fundamental structures of security against eavesdropping have not been fully examined. In a recent paper we identified a geometric feature, namely the extremality of quantum probability distributions, as a necessary and sufficient condition for device independent security. This is the strongest kind of security which does not rely on assumptions on the proper functioning of the physical devices. In the proposed research we want to develop new methods for the study and certification of secure probability distributions. We will also investigate approximately extremal correlations, aiming to show that these can still be used to generate secure keys with a positive rate.