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The formalism of non-commutative quantum mechanics and its extension to many-particle systems

Andreas Hafver

Published Dec 1, 2010• 0 citations
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Abstract

By submitting this thesis electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the owner of the copyright thereof (unless to the extent explicitly otherwise stated) and that I have not previously in its entirety or in part submitted it for obtaining any qualification.

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Mandatory declaration by the author This thesis is composed of my original work, and contains no material previously pub-lished or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant tech-nical procedures, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the General Award Rules of The University of Queensland, im-mediately made available for research and study in accordance with the Copyright Act 1968. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Statement of contributions to jointly authored works contained in the thesis. This thesis presents six jointly authored works that have been published by, or submitted to, peer-reviews scientific journals. Each is presented as a Chapter in this thesis. Follow-ing each is a detailed contribution statement. Statement of contributions by others to the thesis as a whole. No contributions by others.

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It is established that the manipulation of quantum information is bound only by the laws of physics and thus information can be characterised, quantified and processed as a physical entity using the basic properties of quantum mechanics.The most advanced quantum information related technology at present is Quantum Key Distribution (QKD).QKD encodes information into a quantum data carrier, in particular, a single photon that is transported through a quantum channel to produce secure key.To date QKD has been demonstrated across two types of channels which is generally fibre or free space.Free space QKD is beneficial since it provides various mediums for the encoding.When considering the atmosphere as a medium for free space QKD, one of the challenges is the effects of turbulence.Apart from the turbulence effects, one of the other challenges faced with implementing a QKD system, is the use of an appropriate source of single photons for the encoding.A good implementation of a source of single photons would be to make use of entanglement.This thesis addresses the above two aspects of QKD Development of Encoding and Entanglement for Free Space Quantum Key Distribution DECLARATION 1 -PLAGIARISM I, Yaseera Ismail, declare that 1.The research reported in this thesis, except where otherwise indicated, is my original research.2. This thesis has not been submitted for any degree or examination at any other university.3. This thesis does not contain other persons' data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons.4. This thesis does not contain other persons writing, unless specifically acknowledged as being sourced from other researchers.Where other written sources have been quoted, then:(a) Their words have been re-written but the general information attributed to them has been referenced (b) Where their exact words have been used, then their writing has been placed in italics and inside quotation marks, and referenced.5. This thesis does not contain text, graphics or tables copied and pasted from the Internet, unless specifically acknowledged, and the source being detailed in the thesis and in the References sections.

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Mandatory declaration by the author This thesis is composed of my original work, and contains no material previously pub-lished or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant tech-nical procedures, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the General Award Rules of The University of Queensland, im-mediately made available for research and study in accordance with the Copyright Act 1968. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Statement of contributions to jointly authored works contained in the thesis. This thesis presents six jointly authored works that have been published by, or submitted to, peer-reviews scientific journals. Each is presented as a Chapter in this thesis. Follow-ing each is a detailed contribution statement. Statement of contributions by others to the thesis as a whole. No contributions by others.
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii We present an algorithmic framework for parallel quantum circuit synthesis using meet-in-the-middle synthesis techniques. We also present two implementations thereof, using both threaded and hybrid parallelization techniques. We give examples where applying parallelism offers a speedup on the time of circuit synthesis for 2-and 3-qubit circuits. We use a threaded algorithm to synthesize 3-qubit circuits with optimal T-count 9, and 11, breaking the previous record of T-count 7. As the estimated runtime of the framework is inversely proportional to the number of processors, we propose an implementation using hybrid parallel programming which can take full advantage of a computing cluster’s thousands of cores. This implementation has the potential to synthesize circuits which were previously deemed impossible due to the exponential runtime of existing algorithms.
It is established that the manipulation of quantum information is bound only by the laws of physics and thus information can be characterised, quantified and processed as a physical entity using the basic properties of quantum mechanics.The most advanced quantum information related technology at present is Quantum Key Distribution (QKD).QKD encodes information into a quantum data carrier, in particular, a single photon that is transported through a quantum channel to produce secure key.To date QKD has been demonstrated across two types of channels which is generally fibre or free space.Free space QKD is beneficial since it provides various mediums for the encoding.When considering the atmosphere as a medium for free space QKD, one of the challenges is the effects of turbulence.Apart from the turbulence effects, one of the other challenges faced with implementing a QKD system, is the use of an appropriate source of single photons for the encoding.A good implementation of a source of single photons would be to make use of entanglement.This thesis addresses the above two aspects of QKD Development of Encoding and Entanglement for Free Space Quantum Key Distribution DECLARATION 1 -PLAGIARISM I, Yaseera Ismail, declare that 1.The research reported in this thesis, except where otherwise indicated, is my original research.2. This thesis has not been submitted for any degree or examination at any other university.3. This thesis does not contain other persons' data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons.4. This thesis does not contain other persons writing, unless specifically acknowledged as being sourced from other researchers.Where other written sources have been quoted, then:(a) Their words have been re-written but the general information attributed to them has been referenced (b) Where their exact words have been used, then their writing has been placed in italics and inside quotation marks, and referenced.5. This thesis does not contain text, graphics or tables copied and pasted from the Internet, unless specifically acknowledged, and the source being detailed in the thesis and in the References sections.