Measurement of any observable in a quantum mechanical system yields a histogram of the state of
the system in the basis of that observable. Measurements of a judiciously chosen
quorum of appropriate observables of a system that are informationally complete, yield a set of
histograms called a tomogram. In the context of atoms inter- acting with radiation fields, both
the optical tomogram and the tomogram pertaining to atomic observables would yield, in principle,
information about the full system and its subsystems. Quantum state reconstruction seeks to obtain
the density matrix from the tomogram. However, even in the simple case of a bipartite system
comprising two 2-level atoms (two qubits), state reconstruction from relevant tomograms typically
employs statistical tools that are inherently error-prone . The reconstruction procedure is
significantly more difficult in the case of entangled multipartite qubit states . At- tempts at
scalable reconstruction programs for systems with a large number of qubits, and the challenges
faced in this context, have been reported in the literature . It is
therefore desirable to extract information about the state directly from the tomogram, avoiding the
reconstruction procedure. This has been demonstrated in bipartite qubit systems by estimating state
fidelity with respect to a specific target state directly from the tomogram, and comparing the
errors that arise with the cor- responding errors in procedures involving detailed
state reconstruction . Further, efficient methods have been proposed to estimate entanglement
entropies directly from data in the context of qubit systems.
Of particular interest and relevance is the performance of the tomographic entanglement
indicators computed directly from experimental data. In this context, we have examined HQ systems
using the IBM quantum computer and also the spin system mentioned earlier. In the former case,
equivalent circuits that mimic the atomic subsystem of the multipartite HQ system considered, were
provided to the IBM quantum computer for generation of the tomogram. The purpose of this
investigation was to assess the extent to which experimental losses affected entanglement
indicators. In the latter case, the NMR-QIP group in IISER Pune, India, provided us with
experimentally reconstructed density matrices from an NMR spectroscopy. We have
computed the corresponding tomograms and from these, the entanglement indicators. The purpose of
this investigation was to assess, using a simple experimentally viable entangled system, the
limitations that could possibly arise by neglecting the off-diagonal elements of the density
matrix. A significant outcome of this thesis is the identification of useful and reliable
entanglement indicators directly from tomograms in generic quantum systems.
