The research has analysed quantum detection, specifically using Nuclear Magnetic Resonance (NMR) and the Hahn Echo sequence with transmons in IBM Quantum environments, to improve the understanding of quantum entanglement of qubits. Focusing on initialisation in the |+,-> state, the study applied a rigorous theoretical and experimental approach, evaluating purity, the Peres Horodecki criterion, the density matrix and CHSH inequalities. A crucial result of the study is the detection of entanglement within the system, despite a significant discrepancy between the theoretical and experimental density matrices. This suggests that, although entanglement is present, the system does not reach the full theoretical intensity, as evidenced by the non-violation of the CHSH inequalities. The results underline the importance of refining state initialisation and qubit control techniques to ensure robust entanglement. Future research should focus on experimental setups that not only confirm the presence of entanglement through the violation of CHSH inequalities, but also improve its practical applicability in fields such as medical diagnostics and environmental monitoring.