Learning entanglement from tomography data: Contradictory measurement importance for neural networks and random forests

We study the effectiveness of two distinct machine learning techniques, neural networks and random forests, in the quantification of entanglement from two-qubit tomography data. Although we predictably find that neural networks yield better accuracy, we also find that the way the two methods reach their prediction is starkly different. This is seen by the measurements which are the most important for the classification. Neural networks follow the intuitive prediction that measurements containing information about nonlocal coherences are most important for entanglement, but random forests signify the dominance of information contained in occupation measurements. This is because occupation measurements are necessary for the extraction of data about all other density matrix elements from the remaining measurements. The same discrepancy does not occur when the models are used to learn entanglement directly from the elements of the density matrix, so it is the result of the scattering of information and interdependence of measurement data. As a result, the models behave differently when noise is introduced to various measurements, which can be harnessed to obtain more reliable information about entanglement from noisy tomography data.