Measurement plays a fundamental role in quantum physics as it describes the only way we can gain information about a quantum system. Since quantum measurements are invasive, observations will have an impact on its time evolution. On one hand, the unwanted "back action" of measurement can prevent us from extracting all the desired information about a quantum system. On the other hand, the influence of measurement can be used to modify the natural dynamics and drive the system in a desired way. Both of these situations can be formulated very clearly in the context of quantum walks , marking a well-defined playground eliminating the distractions that otherwise often lead to confusing interpretation issues. For example, even a simple question such as what is the probability and how long it takes a quantum walker to reach a certain vertex on the graph — e.g. the initial vertex, offer multiple formulations of the problem yielding distinct results [2-5].
The aim of the thesis would be to explore the impact of observation in general cases, such as on higher dimensional lattices, or multiple walkers (either quantum or classical). Besides providing a deeper insight into the fundamentals of quantum mechanics, the two walker case offers opportunities for applications such as a probabilistic realization of (non-linear) interactions  or error correction [7,8].
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