Applications of coherent classical communication and the Schur transform to quantum information theory

Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information not only yields new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory-coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half. The first part of this thesis (Chapters 1-4) is in fact built around two loosely overlapping themes. One is quantum Shannon theory, a broad class of coding theorems that includes Shannon and Schumacher data compression, channel coding, entanglement distillation and many others. The second, more specic, theme is the concept of using unitary quantum interactions to communicate between two parties. We begin by presenting new formalism: a general framework for Shannon theory that describes communication tasks in terms of fundamental information processing resources, such as entanglement and classical communication. Then we discuss communication with unitary gates and introduce the concept of coherent classical communication, in which classical messages are sent via some nearly unitary process. We find that coherent classical communication can be used to derive several new quantum protocols and unify them both conceptually and operationally with old ones.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Harrow, Aram (Aram Wettroth), 1980-

Advisor dc:contributor.advisor

• Isaac L. Chuang.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34973

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34973