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978-3-8439-1181-8, Reihe Physik
Christof J. Happ
Adaptive and Non-Adaptive Estimation of Discrete Quantum States
182 Seiten, Dissertation Universität Ulm (2013), Hardcover, A5
￼Quantum information theory strives to apply quantum mechanics to computer technology. Its holy grail is the construction of a universal quantum computer or at least a quantum simulator.
It is vital to efficiently retrieve the quantum information acquired with such a computer or simulator. Compared to classical systems, there are fundamental differences in how information is treated in quantum-mechanical systems which make quantum information a valuable resource, and the question how to efficiently deal with it an essential research topic.
This work studies methods to efficiently extract state information from a limited amount of discrete systems prepared in the same quantum state. We will investigate methods to adaptively choose the measurements themselves in order to improve estimation quality. Thus, our aim is not only to optimise the estimate to agree as well as possible with the measurement data, but also the measurement parameters to produce the most informative results.
The investigated estimation procedures are independent of the dimensionality of the used systems. We present simulation results for up to 23 dimensions.
We introduce an adaption scheme that emulates the success of mutually unbiased measurements. It does not only succeed in doing this for dimensions for which not even a complete set of mutually unbiased bases is known; but it is also applicable for more measurement ste