Aspects of Quantum Steering

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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.