Exploring Quantum Entanglement in Dileptonic $H \rightarrow WW^*$ Final States with ATLAS at $\sqrt{s} =13\, \text{TeV}$

According to the Standard Model, $W$ boson pairs produced in Higgs decays are entangled. This property has not yet been probed experimentally. To probe quantum entanglement in $W$ boson pairs, it is suitable to first exclude the hypothesis of a separable state. The Standard Model hypothesis is treated as pseudo data in this thesis. Since electrons and muons can be measured precisely the dileptonic decay channel with one electron and one muon in the final state is used. To investigate quantum entanglement, sensitive variables with a clear difference between the separable and entangled state must be known. The studied observables are $m_{ll}$, $\phi_{ll}$ and $\eta_{ll}$. For the signal and background separation, a dense neural network is used. To compare the two hypotheses, a binned profile likelihood unfolding and a $\chi^2$ hypothesis test is performed. The most sensitive observable is $m_{ll}$. It provides exclusion limits for the hypothesis of a separable state of $6\sigma$ ($4.3\sigma$) using only statistical uncertainties (including systematic uncertainties). The observable, $\phi_{ll}$, is less sensitive to quantum entanglement with $5.7\sigma$ ($3.7\sigma$) exclusion limits for the separable state using only statistical uncertainties (including systematic uncertainties). The least sensitive studied observable is $\eta_{ll}$. The exclusion limit for a separable state using this observable is less than $1 \sigma$.