My dissertation consists of two independent parts. Part one of my dissertation examines concepts of quantum information. I clarify three very different concepts of information and assess their implications for understanding quantum mechanics. First I clarify the concept of information due to Shannon, and its relation to physical theories. Using the Shannon concept, I examine two purportedly new concepts of quantum information. I argue that a fundamental philosophical mistake is made regarding these concepts. Advocates of these new concepts do not properly distinguish between the properties of information due to the physical medium it is stored in from the properties of information per se. This distinction is crucial for developing a new concept to help us understand quantum mechanics and evaluating its merits.
Part two of my dissertation examines explanations of the efficiency that quantum computers enjoy over classical computers for some computational tasks, and the relationship between explanations of efficiency and interpretations of quantum mechanics. I examine the so-called quantum parallelism thesis, that quantum computers can perform many computations in a single step, a feat thought not to be possible on classical computers. The truth of this thesis is not obvious, and contested by some. I develop a set of general criteria for computation that any computing device must satisfy. I use these criteria to demonstrate that the quantum parallelism thesis is true. As an application of these general criteria for computation I articulate three distinct concepts of parallelism and demonstrate that classical computers can compute in parallel as well. This demonstrates that the truth of the quantum parallelism thesis alone does not provide a complete explanation of the efficiency of quantum computers. I supplement the quantum parallelism thesis to provide a complete explanation. Finally, I address the claim that only the many-worlds interpretation of quantum mechanics can underwrite the truth of the quantum parallelism thesis. The general criteria for computation provide support for the quantum parallelism thesis independent of any interpretation of quantum mechanics.
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-12082004-025939 |
| Date | 31 January 2005 |
| Creators | Duwell, Armond James |
| Contributors | John Norton, John Earman, Laura Reutsche, Jeff Bub |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-12082004-025939/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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