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QUANTUM CODING WITH ENTANGLEMENT
by
Mark McMahon Wilde
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements of the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2008
Copyright 2008 Mark McMahon Wilde
Object Description
| Title | Quantum coding with entanglement |
| Author | Wilde, Mark McMahon |
| Author email | mark.wilde@usc.edu; mwilde@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Electrical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2008-06-17 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-07-31 |
| Advisor (committee chair) | Brun, Todd A. |
| Advisor (committee member) |
Lidar, Daniel Haas, Stephan |
| Abstract | Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the theory of quantum error correction -- mainly to the theory of "entanglement-assisted'' quantum error correction where the sender and receiver share entanglement in the form of entangled bits (ebits) before quantum communication begins. Our first contribution is an algorithm for encoding and decoding an entanglement-assisted quantum block code. We then give several formulas that determine the optimal number of ebits for an entanglement-assisted code. The major contribution of this thesis is the development of the theory of entanglement-assisted quantum convolutional coding. A convolutional code is one that has memory and acts on an incoming stream of qubits. We explicitly show how to encode and decode a stream of information qubits with the help of ancilla qubits and ebits. Our entanglement-assisted convolutional codes include those with a Calderbank-Shor-Steane structure and those with a more general structure. We then formulate convolutional protocols that correct errors in noisy entanglement. Our final contribution is a unification of the theory of quantum error correction -- these unified convolutional codes exploit all of the known resources for quantum redundancy. |
| Keyword | entanglement-assisted quantum error correction; quantum convolutional coding; convolutional entanglement distillation |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1491 |
| Rights | Wilde, Mark McMahon |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Wilde-2106 |
| Archival file | uscthesesreloadpub_Volume32/etd-Wilde-2106.pdf |
Description
| Title | Page 1 |
| Full text | QUANTUM CODING WITH ENTANGLEMENT by Mark McMahon Wilde A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements of the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2008 Copyright 2008 Mark McMahon Wilde |
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