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.

💡 Research Summary

This dissertation presents a comprehensive study of quantum correlations and open‑system dynamics using solution‑state nuclear magnetic resonance (NMR) as a versatile experimental platform. The work is organized into four main projects, each addressing a distinct aspect of quantum physics while exploiting the long T₁ and T₂ relaxation times and high‑fidelity radio‑frequency control available in nuclear spins.

The first project investigates temporal quantum correlations through the Leggett‑Garg inequality (LGI). By employing a three‑qubit register (two system qubits and one ancilla) the authors realize a superposition of distinct unitary evolutions, Û = αU₁ + βU₂, with |α|² + |β|² = 1. This “superposed unitary” dynamics leads to LGI violations that exceed the standard quantum bound of 1.5, reaching values around 1.78. Moreover, the superposition provides enhanced robustness against decoherence: the LGI violation persists for a significantly longer time compared with a single‑unitary evolution under identical noise conditions. The experimental results are supported by a theoretical analysis of higher‑order LGIs and the construction of general superposed channels.

The second project focuses on Lee‑Yang (LY) zeros, the complex‑plane zeros of the partition function that encode critical behavior. The authors propose a method to extract the full set of LY zeros of an asymmetric two‑spin Ising model using a single quantum probe (the third spin). By initializing the probe at various points on the complex “co‑amoeba” plane and monitoring the mutual information between probe and system, they identify the times at which the mutual information peaks; these times correspond precisely to the LY zeros. Experiments on a three‑qubit NMR register confirm the complete reconstruction of the LY zero set for both symmetric (h_A = h_B) and asymmetric (h_A ≠ h_B) field configurations, demonstrating a direct link between quantum correlations and thermodynamic singularities.

The third project explores the quantum Mpemba effect in nuclear‑spin relaxation. The Mpemba effect, originally observed in classical thermodynamics, describes the counter‑intuitive situation where a system farther from equilibrium relaxes faster than one that is closer. Using NMR, the authors prepare two distinct initial polarization states of a spin ensemble: one near the thermal equilibrium and another far from it. By measuring longitudinal relaxation (T₁) curves simultaneously, they observe that the far‑from‑equilibrium state reaches the steady state more quickly, confirming the quantum Mpemba effect without any engineered bath. Theoretical modeling based on open‑system master equations explains the phenomenon as a consequence of differing spectral overlaps with the environmental noise spectrum.

The final project examines entanglement localization and delocalization induced by local interactions, which seemingly leads to a violation of the quantum data‑processing inequality (QDPI). By coupling a non‑interacting pair of spins to a third probe spin via a local Ising interaction, entanglement is transferred from the probe to the pair. During this process the mutual information between the probe and the pair appears to increase beyond the bound set by QDPI, suggesting an apparent violation. However, the authors construct an explicit completely positive trace‑preserving (CPTP) map that captures the full three‑spin dynamics, showing that the inequality holds when the total system is considered. This resolves the apparent paradox and highlights the importance of accounting for hidden degrees of freedom in quantum information flow analyses.

Overall, the thesis demonstrates that nuclear‑spin NMR is an exceptionally powerful testbed for probing subtle quantum phenomena that span quantum foundations, statistical physics, non‑equilibrium thermodynamics, and quantum information theory. The four studies not only provide experimental verification of theoretical predictions—such as super‑unitary‑enhanced non‑macrorealism, full LY‑zero reconstruction, quantum Mpemba relaxation, and entanglement‑mediated QDPI apparent violations—but also open new avenues for quantum simulation, error‑resilient control, and the design of novel quantum technologies. Future work suggested includes scaling the methods to larger spin networks, integrating error‑correction schemes with superposed channels, and exploiting the Mpemba effect for rapid state preparation in quantum processors.