From the Theory of Entanglement to the Practice of Optical Quantum Information
Abstract
This thesis consolidates my research on several topics of quantum information. We start with an analysis of negativity, an entanglement monotone making appearances throughout the thesis. Because negativity is a nonanalytic function of a density matrix, prior methods in the physics literature have been insufficient to compute its derivatives. After developing techniques in complex, patterned matrix calculus, we write down a perturbative expansion of negativity to any order. We continue with another problem in entanglement theory: characterizing the states for which all local actions on one subsystem can be replicated by actions on another. Our results lead to a method for quantifying entanglement based on operational symmetries and tie in to concepts in quantum mechanics, quantum field theory, and classical optics. The study of local operations on entangled states continues with an investigation of the local equivalence of special subsets of graph states, including those that underlie the all-photonic quantum repeater. I show, for certain repeater-like graph states, that equivalence through local unitaries implies equivalence through local Clifford unitaries, investigate certain other properties, and offer alternative proofs and clarifications on existing results. Armed with a better understanding of repeater graph states, I give a blueprint for near-term long-distance all-photonic quantum communication. I make the case that an intercity communication scheme based on a…
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