Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


diss15.pdf (2.2 MB)

ETD Abstract Container

Abstract Header

Convex Geometric Connections to Information Theory

Jenkinson, Justin
http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413

Abstract Details

2013, Doctor of Philosophy, Case Western Reserve University, Mathematics.
Convex geometry is a field of mathematics that has experienced rapid growth in recent years and has proven to be an extremely useful perspective in areas of research. Problems in many different fields can be interpreted geometrically which often leads to powerful and surprising results. This thesis establishes connections between convex geometry and both classical and quantum information theory. We introduce the mean width bodies and illustrate the geometric interpretation they provide for the relative entropy of cone measures of a convex body and its polar. We define relative entropy for convex bodies and its relation to affine isoperimetric inequalities is considered. Other connections are made by considering quantum information theory. The fundamental objects in quantum information theory are quantum states. The set of states is convex as are some of its important subsets. Therefore, convex geometry provides a natural approach to explore quantum states. Fairly sharp estimates are obtained regarding the geometry of quantum states using basic notions in convex geometry. In particular, the distance between the set of states with positive partial transpose and the set of separable states is explored. Finally, the optimal constants for the spherical isoperimetric inequality are provided and generalizations of a concentration inequality are suggested.
Stanislaw Szarek (Advisor)
Elisabeth Werner (Advisor)
Mathematics

Recommended Citations

Citations

  • Jenkinson, J. (2013). Convex Geometric Connections to Information Theory [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413

    APA Style (7th edition)

  • Jenkinson, Justin. Convex Geometric Connections to Information Theory. 2013. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413.

    MLA Style (8th edition)

  • Jenkinson, Justin. "Convex Geometric Connections to Information Theory." Doctoral dissertation, Case Western Reserve University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413

    Chicago Manual of Style (17th edition)

case1365179413
1,003
© , all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.