Generation and Uses of Distributed Entanglement in Quantum Information

In this thesis, we focus on the questions of how quantum entanglement can be generated between two spatially separated systems and, once generated, how it can be applied in quantum metrology. First we will discuss a protocol for the generation of large entangled states using long range interactions. Next, we will turn our attention to more general questions of how the Lieb-Robinson bound and other limitations on entanglement can be used to inform the design of quantum computers. We will present a proposed graph architecture, the hierarchical product, which we believe provides excellent balance between requiring large amounts of communication interaction and being able to perform computations quickly. Finally, we will look at the scenario of quantum sensing. In particular, we will examine protocols for quantum function estimation, where quantum sensors are available to measure all of the inputs to the function. We will demonstrate that entangled sensors are more capable than non-entangled ones by first deriving a new lower bound on measurement error and then presenting protocols that saturate these bounds.