Aspects of Quantum Steering

1935年，Schrödinger指出，一个实验者通过局部测量来影响另一个分离的量子系统的能力，是爱因斯坦-波多尔斯基-罗森论证的核心。虽然这并不允许传输信息，但他对这种远距离的作用很着迷，并称之为“量子导向”。在现代观点中，量子转向是一种与纠缠和贝尔非局域性相关但独立的量子相关形式。此外，量子转向已被证明与量子基础和量子信息处理中的许多主题直接相关，如测量不兼容和量子密码学。在这个项目中，我们将研究量子转向的几个方面。在第一部分中，我们将使用量子信息理论的技术来描述量子转向。更具体地说，我们将提供从熵不确定性关系中检测转向的标准。此外，我们的目标是从可操纵性的结果中推导出熵的不确定性关系。在第二部分中，我们将基于几何方法，以抽象的方式研究量子转向。这将导致新的算法和分析工具，以表征在高维系统的转向。此外，我们将研究转向的量化，并讨论在量子信息处理中的应用。该项目将导致对量子转向及其与不确定性关系的联系的新理解。这将使人们对不对称情况下的量子信息处理有新的认识，并可能导致对旨在产生量子相关性的实验进行更好的分析。

In 1935, Schrödinger noted that the ability of one experimenter to affect another separated quantum system by performing measurements locally is central to the Einstein-Podolsky-Rosen argument. Although this does not allow to transmit information, he was fascinated by this kind of action at a distance and called it ``quantum steering''. In the modern view, quantum steering is a form of quantum correlations related to, but independent of, entanglement and Bell non-locality. Moreover, quantum steering has been proven to be directly connected to many topics in quantum foundations and quantum information processing, such as measurement incompatibility and quantum cryptography.In this project we will investigate several aspects of quantum steering. In the first part, we will characterize quantum steering using techniques from quantum information theory. More specifically, we will provide criteria for the detection of steering from entropic uncertainty relations. In addition, we aim at deriving entropic uncertainty relations from results on steerability. In the second part we will study quantum steering in an abstract manner, based on a geometrical approach. This will lead to novel algorithms and analytical tools to characterize steering in high-dimensional systems. Moreover, we will study the quantification of steering and discuss applications to quantum information processing. The project will result in a novel understanding of quantum steering and its connection to uncertainty relations. This will enable new insights into quantum information processing in asymmetric scenarios and may lead to a better analysis of experiments aiming at the generation of quantum correlations.