Investigations on Quantum Correlations and Open Quantum System Dynamics Through Nuclear Spins

Nuclear spins provide an ideal platform for studying quantum correlations and open quantum system dynamics across diverse areas, including quantum information, quantum foundations, and many-body physics. This is enabled by their long longitudinal (T1) and transverse (T2) coherence times and precise control using radio frequency pulses. In this thesis, I present my work using nuclear spins to explore these themes. First, I study temporal quantum correlations quantified by the Leggett Garg inequality (LGI) for a qubit evolving under a superposition of unitary operators. Using a three qubit quantum register, we experimentally realized superposed unitaries and observed LGI violations exceeding the maximal quantum bound of 1.5, indicating enhanced non-classicality. Notably, this superposed unitary dynamics also showed improved robustness against decoherence. Next, I investigate Lee Yang zeros, which are zeros of the partition function in the complex plane that reveal thermodynamic behavior near criticality. We proposed and experimentally demonstrated a method to determine the full set of Lee Yang zeros of an asymmetric Ising model using a single quantum probe in a three-qubit nuclear spin register. We further showed that the mutual information between the probe and system peaks at times corresponding to these zeros. I then report our study of the quantum Mpemba effect in nuclear spin relaxation, where systems farther from equilibrium can relax faster than those closer to steady state, verified both theoretically and experimentally using NMR. Finally, I discuss our work on entanglement localization and delocalization induced by local interactions, leading to an apparent violation of the quantum data processing inequality. We showed that this violation is only apparent by constructing a completely positive and trace preserving map describing the dynamics.