Signatures of Nonclassical Effects in Tomograms

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.