Page 1 |
Save page Remove page | Previous | 1 of 168 | Next |
|
small (250x250 max)
medium (500x500 max)
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
Subset |
TOPICS IN QUANTUM CRYPTOGRAPHY, QUANTUM ERROR
CORRECTION, AND CHANNEL SIMULATION
by
Zhicheng Luo
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
May 2009
Copyright 2009 Zhicheng Luo
Object Description
| Title | Topics in quantum cryptography, quantum error correction, and channel simulation |
| Author | Luo, Zhicheng |
| Author email | zluo@usc.edu; zhicheng.luo@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Physics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-09-02 |
| Date submitted | 2009 |
| Restricted until | Unrestricted |
| Date published | 2009-05-04 |
| Advisor (committee chair) | Devetak, Igor |
| Advisor (committee member) |
Haas, Stephan Brun, Todd Dappen, Werner Lidar, Daniel |
| Abstract | In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50].; For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms.; For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length.; For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol.; For the fourth topic, we study and solve the problem of classical channel simulation with quantum side information at the receiver. Our main theorem has two important corollaries: rate-distortion theory with quantum side information and common randomness distillation. Simple proofs of achievability of classical multi-terminal source coding problems can be made via a unified approach using the channel simulation theorem as building blocks. The fully quantum generalization of the problem is also conjectured with outer and inner bounds on the achievable rate pairs. |
| Keyword | quantum cryptography; quantum error correction; secret communication; channel simulation |
| 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 |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m2117 |
| Rights | Luo, Zhicheng |
| 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-Luo-2710 |
| Archival file | uscthesesreloadpub_Volume17/etd-Luo-2710.pdf |
Description
| Title | Page 1 |
| Full text | TOPICS IN QUANTUM CRYPTOGRAPHY, QUANTUM ERROR CORRECTION, AND CHANNEL SIMULATION by Zhicheng Luo A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) May 2009 Copyright 2009 Zhicheng Luo |
Comments
Post a Comment for Page 1
