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Upper and lower bounds on quantum codes.

Smith, Graeme Stewart Baird.

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Upper and lower bounds on quantum codes.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Upper and lower bounds on quantum codes./
Author:	Smith, Graeme Stewart Baird.
Description:	70 p.
Notes:	Adviser: John Preskill.
Contained By:	Dissertation Abstracts International67-09B.
Subject:	Computer Science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3235592
ISBN:	9780542893360

Upper and lower bounds on quantum codes.
Smith, Graeme Stewart Baird.

Upper and lower bounds on quantum codes. - 70 p.

Adviser: John Preskill.

Thesis (Ph.D.)--California Institute of Technology, 2006.

Chapter 5 describes an equivalence between a family of noisy preprocessing protocols for quantum key distribution and entanglement distillation protocols whose target state belongs to a class of private states called "twisted states."

ISBN: 9780542893360Subjects--Topical Terms:

626642
Computer Science.

Upper and lower bounds on quantum codes.
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005 20110906
008 110906s2006 eng d
020 $a 9780542893360
035 $a (UnM)AAI3235592
035 $a AAI3235592
040 $a UnM $c UnM
100 1 $a Smith, Graeme Stewart Baird. $3 1288093
245 1 0 $a Upper and lower bounds on quantum codes.
300 $a 70 p.
500 $a Adviser: John Preskill.
500 $a Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5125.
502 $a Thesis (Ph.D.)--California Institute of Technology, 2006.
520 $a Chapter 5 describes an equivalence between a family of noisy preprocessing protocols for quantum key distribution and entanglement distillation protocols whose target state belongs to a class of private states called "twisted states."
520 $a In Chapter 6, the codes of Chapter 4 are combined with the protocols of Chapter 5 to provide higher key rates for one-way quantum key distribution than were previously thought possible.
520 $a This thesis provides bounds on the performance of quantum error correcting codes when used for quantum communication and quantum key distribution. The first two chapters provide a bare-bones introduction to classical and quantum error correcting codes, respectively. The next four chapters present achievable rates for quantum codes in various scenarios. The final chapter is dedicated to an upper bound on the quantum channel capacity.
520 $a Chapter 3 studies coding for adversarial noise using quantum list codes, showing there exist quantum codes with high rates and short lists. These can be used, together with a very short secret key, to communicate with high fidelity at noise levels for which perfect fidelity is, impossible.
520 $a Chapter 4 explores the performance of a family of degenerate codes when used to communicate over Pauli channels, showing they can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code and that exceed those of previously known degenerate codes. By studying the scaling of the optimal block length as a function of the channel's parameters, we develop a heuristic for designing even better codes.
520 $a Finally, Chapter 7 presents a new upper bound on the quantum channel capacity that is both additive and convex, and which can be interpreted as the capacity of the channel for communication given access to side channels from a class of zero capacity "cloning" channels. This "clone assisted capacity" is equal to the unassisted capacity for channels that are degradable, which we use to find new upper bounds on the capacity of a depolarizing channel.
590 $a School code: 0037.
650 4 $a Computer Science. $3 626642
650 4 $a Engineering, Electronics and Electrical. $3 626636
650 4 $a Physics, General. $3 1018488
690 $a 0544
690 $a 0605
690 $a 0984
710 2 0 $a California Institute of Technology. $3 726902
773 0 $t Dissertation Abstracts International $g 67-09B.
790 $a 0037
790 1 0 $a Preskill, John, $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3235592