Analyzing the correlation structure of quantum systems is central to understanding their behaviour. The notion of sector lengths is useful for quantifying correlations in multipartite quantum systems in a basis-independent manner. A complete characterization for sector lengths for two and three qubits exists, however for more qubits this proves difficult to obtain. Instead of deriving properties for four qubits and above, we numerically investigate such systems by obtaining lower bounds on the maximal $k$-partite correlations for certain $k > 3$. For this purpose, tools from differential geometry are introduced to optimize over arbitrary pure quantum states and certain subsets such as symmetric states. Additionally, we numerically investigate and support a given conjecture of a threshold $n_0$ after which correlations are upper bounded by $\binom{n}{k}$. We obtain results for the investigation of this threshold $n_0$ and if it can be discovered using the subsets of pure states.
BSc Thesis - Numerical bounds on few body sector-lengths
