Title: Bell inequalities and large-scale quantum networks
Abstract: In the field of quantum information theory one investigates the properties of information carriers which are subject to the laws of quantum mechanics. The differences between quantum mechanics and the laws that govern macroscopic information carriers lead to new opportunities and challenges in information processing.
One of these differences is the entanglement of particles, which leads to strong correlations of measurement outcomes. This allows the violation of so-called Bell inequalities in quantum mechanics, which is impossible in ``classical'' theories. I investigated the possible amount of violation for an important class of Bell inequalities. In doing so I found a simple mathematical expression for an upper bound and studied the achievability of that bound. The approach provides a basic understanding of the considered Bell inequalities, which allows to construct new inequalities with interesting properties. In particular one can understand how Bell inequalities allow to bound the dimension of a quantum system. Changing a Bell inequality with invariant quantum value proved useful in optimizing them with respect to the violation.
The distribution of entangled systems across large distances is achieved by sending photons. However, since they are absorbed in long fibers, quantum repeater become necessary for distances larger than approximately 200 km. Several approaches to counter the losses are known. In the long term error correction codes are very promising. Here the information is encoded into many photons, such that some losses can be compensated. I contributed to the analysis of this approach by showing how it naturally generalizes to networks of quantum repeaters. The formalism of graph states is useful in this context. A complete performance analysis of a quantum repeater contains many sources of errors and their propagation inside the circuit. I extended this analysis compared to the literature. At the moment it is not clear which types of quantum repeaters will prevail. My comparison of different theoretical proposals helps towards answering this question.
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: dissertation
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