Title:
|
Convex Set Approximation Problems in Quantum Information |
Author:
|
Fernandes, Eric
|
Department:
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Department of Mathematics and Statistics |
Program:
|
Mathematics and Statistics |
Advisor:
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Pereira, Rajesh Zeng, Bei |
Abstract:
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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 |
Terms of Use:
|
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