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Unification of quantum information theory

Citation

Abeyesinghe, Anura Yamesh (2006) Unification of quantum information theory. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05252006-222551

Abstract

We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the "mother" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol(FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:quantum information theory; quantum shannon theory; unification
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Mabuchi, Hideo
  • Wise, Mark B.
  • McAfee, R. Preston
Defense Date:23 May 2006
Author Email:andrew55555 (AT) gmail.com
Record Number:CaltechETD:etd-05252006-222551
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05252006-222551
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2063
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:31 May 2006
Last Modified:26 Dec 2012 02:46

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