Tomographic entanglement indicators from NMR experiments

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 nuclear magnetic resonance (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 and carry out a similar comparative assessment of the performance of tomographic indicators. 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. Published under an exclusive license by AIP Publishing.

Automated summary

In this paper, the performance of entanglement indicators obtained from tomograms in spin systems is assessed. Experimental data from nuclear magnetic resonance (NMR) experiments are used to compare these indicators with standard entanglement measures. The study finds that these indicators can reproduce the gross features of entanglement dynamics and spin squeezing properties. However, the tracking of entanglement during time evolution is highly sensitive to the nature and strength of interactions as well as system partitioning. The findings also show that the tomographic approach can estimate entanglement without detailed state reconstruction procedures.