A C*-Algebraic Approach to Quantum Coding Theory.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2008)
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|Item Type:||Ph.D. Thesis|
|Title:||A C*-Algebraic Approach to Quantum Coding Theory|
This work has reached several results. The first is, that it was possible to find a new, algebraic frame in which we can formulate stabilizer codes and show, that the choice of generators of a stabilizer algebra corresponds to choosing a representation of finitely many Rademacher functions in a matrix algebra. The second part of this work was to develop a quantum coding theory as a quantum analogue of classical coding theory. We do this by using a systematical view of quantum probability theory that was introduced by Kümmerer . We follow this way of algebraization and develop analogously a quantum coding theory. Our result differs in some points from what has been developed so far, mainly because we are working not only with pure but also arbitrary states as well as infinitely many coupled qubits. We were able to integrate the common examples of quantum codes into our theory. The third main result is that we were able to show that the most important quantum algorithms, including stabilizer codes and the Shor algorithm, are in some sense commutative and thus classical. This could be done as quantum algorithms fit into the notion of quantum measurements, and our calculations imply that they can be represented as a coupling to a classical Bernoulli shift.  B. Kümmerer, Markov Dilations on W*-Algebras, Journal Functional Analysis, 63:139-177, 1985.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||quantum coding theory, quantum code, stabilizer code, C*-Algebra, AF-algebra, code, coder, qubit, quantum algorithm, convolutional code, quantum measurement, algebraization, Shor algorithm, essentially commutative|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 530 Physik
000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik
500 Naturwissenschaften und Mathematik > 510 Mathematik
|Divisions:||04 Department of Mathematics|
|Date Deposited:||17 Oct 2008 09:23|
|Last Modified:||07 Dec 2012 11:54|
|Referees:||Kümmerer, Prof. Dr. Burkhard and Maassen, Dr. Hans|
|Refereed:||3 September 2007|