Year: 2021
Type: dissertation
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.
Author: Eric Baracho Dore Fernandes
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3095803296