  In recent years, the performance of different entanglement indicators
obtained directly from tomograms has been assessed in continuous-variable and
hybrid quantum systems. In this paper, we carry out this task in the case of
spin systems. We compute the entanglement indicators from actual experimental
data obtained from three liquid-state NMR experiments, and compare them with
standard entanglement measures calculated from the corresponding density
matrices, both experimentally reconstructed and numerically computed. The gross
features of entanglement dynamics and spin squeezing properties are found to be
reproduced by these entanglement indicators. However, the extent to which these
indicators and spin squeezing track the entanglement during time evolution of
the multipartite systems in the NMR experiments is very sensitive to the
precise nature and strength of interactions as well as the manner in which the
full system is partitioned into subsystems. We also use the IBM quantum
computer to implement equivalent circuits that capture the dynamics of the
multipartite system in one of the NMR experiments. We compute and compare the
entanglement indicators obtained from the tomograms corresponding to the
experimental execution and simulation of these equivalent circuits. This
exercise shows that these indicators can estimate the degree of entanglement
without necessitating detailed state reconstruction procedures, establishing
the advantage of the tomographic approach.
