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

TL;DR

The thesis investigates quantum correlations and open-system dynamics in nuclear spins using solution-state NMR. It develops and demonstrates three intertwined threads: (i) enhanced non-macrorealism via superposed unitaries that push LGI violations beyond the temporal Tsirelson bound and improve robustness to decoherence; (ii) a quantum-probe protocol to extract the full algebraic variety of Lee–Yang zeros in asymmetric Ising models, linking LY zeros to real-time probe coherence and mutual information; and (iii) natural quantum Mpemba effects and the localization/delocalization of entanglement, clarifying apparent violations of the quantum data-processing inequality with completely positive reduced dynamics. The work combines theory and three-qubit (and four-qubit) NMR experiments to validate concepts and suggests paths for quantum sensing, robust quantum control, and scalable entanglement storage. Overall, it advances understanding of fundamental quantum correlations in open systems and provides practical quantum-simulation–driven tools for complex many-body phenomena.

Abstract

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.

Figures (24)

• Figure 1: Pictorial representation of the contents of this thesis.
• Figure 2: Any quantum experiment can be described in terms of three steps: preparation (which corresponds to fixing the initial state $\rho$ of the system), operation (which can be any CPTP quantum channel $\Phi$, in general) and finally measurement (described by a POVM $\{F_n \}$). After the experiment, only one of the possible outcomes occurs in a given run of the experiment.
• Figure 3: (a) A cartoon representation of the cone $\mathcal{C}_{+}(\mathbb{H}_2)$ in $\mathbb{R}^4$, which is cut by a hypersurface $r_0=1/2$ to obtain the Bloch sphere shown in (b)
• Figure 4: Typical steps involve in the initiation of a solution state NMR experiment. The sample is first dissolved in an appropriately chosen solvent, and then the solution is put in an NMR tube where it stretches to a height of $4-6$ cm. The tube is then put inside the NMR spectrometer where it stands vertically (along $\hat{z}$ axis) in alignment with the strong magnetic field ($B_0 = 11.7$ T).
• Figure 5: (a) Superposition of two unitaries $U_0$ and $U_1$ (for $\phi=\pi/2$) on the Bloch sphere shifts the rotation axis (thick arrow) and introduces nonlinearities in SOE (modeled by the gap in the spokes). (b-d) SOE for the initial state $\vert{0}\rangle$ against final time $t_f$ for different values of $\alpha$ and $\phi$ at $\omega=1$.