Resources in Quantum Technology: Applications in quantum tomography and clock synchronization

Mark De Burgh (2011). Resources in Quantum Technology: Applications in quantum tomography and clock synchronization PhD Thesis, School of Mathematics & Physics, The University of Queensland.

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s40812393_PhD_finalabstract.pdf s40812393_PhD_finalabstract.pdf application/pdf 16.96KB 1
s40812393_PhD_finalthesis.pdf s40812393_PhD_finalthesis.pdf application/pdf 1.75MB 6
Author Mark De Burgh
Thesis Title Resources in Quantum Technology: Applications in quantum tomography and clock synchronization
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2011-02
Thesis type PhD Thesis
Supervisor Dr Andrew Doherty
Prof. Gerard Milburn
Total pages 178
Total colour pages 14
Total black and white pages 164
Subjects 01 Mathematical Sciences
Abstract/Summary Quantum technologies in the areas of metrology, cryptography and computation, both theoretical and practical, are exceeding the limits that are classically possible, and even approaching the ultimate quantum limits. Despite rapid advances, experimental implementation of these technologies remains limited to small systems. The key question of this thesis is whether, through the use of alternate resources, quantum technologies can be brought closer to experimental feasibility. We investigate two application areas: quantum tomography, the experimental characterization of a quantum state or processes and quantum clock synchronization. Quantum tomography is fundamental to all quantum technologies, yet experimentalists have prepared quantum states that surpass existing characterization techniques. A key result of this dissertation is that popular experimental techniques can be improved through an alternative choice of measurement settings based on the geometry of Platonic solids. The change requires no increased complexity in the experimental apparatus. We also derive a novel numerical technique for reconstructing quantum states and processes from measured data. We frame the problem as a semidefinite program, an optimization problem that may be solved efficiently. We also develop a novel adaptive tomography technique, in which the time spent on each measurement adapts based on previous measurement outcomes. Finally to understand the average performance of different tomography schemes we need a notion of a prior distribution over quantum states. We derive a new prior over quantum states based on a recently derived state distinguishability measure, the quantum Chernoff bound. The best classical algorithms to synchronize clocks achieve the so called standard quantum limit. Quantum clock synchronization protocols have already surpassed this limit and theoretical proposals even reach the ultimate Heisenberg limit. However, these protocols rely on a resource known as entanglement, limiting their current feasibility. We develop a novel quantum clock synchronization protocol with performance close to the Heisenberg limit yet requiring no entanglement. We also develop an optical proof of principle realization of the clock synchronization scheme that requires only existing experimental apparatus.
Keyword quantum clock synchronization
quantum chernoff prior distributions
quantum tomography
adaptive tomography
ticking qubits
semidefinite program
maximum likelihood quantum tomography
Additional Notes Page Numbers (of pdf document not thesis) 64,81,87,90,94,100,102,123,124,126,143,151,153,157

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Created: Thu, 10 Feb 2011, 20:18:55 EST by Mr Mark De Burgh on behalf of Library - Information Access Service