Is quantum steering spooky?

Abstract

In quantum mechanics, if one party performs a measurement on one system, different outcomes can lead to different states for another system. This phenomenon is known as quantum steering. The thesis begins with some general results about steering: a classification of which states permit the most powerful type of steering, and the implications of this for quantum correlations. The first main topic is steering in two-qubit systems. It turns out that steering provides an excellent way to visualize two-qubit states, leading to a novel criteria for entanglement and a better understanding of separable states. Oddly, the structure of steering can be more subtle in separable states than it can be in entangled ones. Returning to general quantum systems, I then turn to the EPR paradox, and its generalisation using Local Hidden State models. I show that the lack of such models can be used to quantify the amount of entanglement shared by two parties, even when one of them does not trust their measuring devices. Finally, the desire to understand steering without invoking "spooky action-at- a-distance" leads to the idea that quantum states are states of knowledge. I explore some de Finetti theorems that help to make sense of this idea, but then show a significant roadblock the most natural formalisation of it. The main results in chapters 3 and 4 appear in [JPJR13] and [Pus13] respectively. The result in chapter 6 was improved in collaboration with my supervisors and published in [PBR12].