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Convex Set Approximation Problems in Quantum Information

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Title: Convex Set Approximation Problems in Quantum Information
Author: Fernandes, Eric
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Pereira, RajeshZeng, Bei
Abstract: This thesis investigates methods to approximate convex sets which involve minimizing the Hausdorff metric between a set and certain subsets. We begin by giving a lower bound for the Hausdorff metric between a hypersphere and a circumscribed simplex. We show that this bound is achieved by the regular simplex. Next, we form a lower bound on the Hausdorff distance between the convex hull of the joint numerical range of positive operator valued-measures and the probability simplex. An entanglement witness is a linear functional that separates the convex compact set of separable states from certain entangled states in the Hilbert space. We investigate the applications of our methods by exploring the problem of finding a polytope generated by entanglement witnesses that has minimal distance to the set of separable states.
URI: http://hdl.handle.net/10214/17963
Date: 2020-05-21
Rights: Attribution 4.0 International
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Attribution 4.0 International Except where otherwise noted, this item's license is described as Attribution 4.0 International