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

Abstract

In the presence of a high magnetic field, nuclear spins serve as an ideal testbed for studying quantum correlations and open quantum system dynamics in various physical phenomena ranging from quantum information processing and quantum foundations to quantum many-body physics. This is primarily due to the long classical (T1) and quantum (T2) memories of nuclear spins and robust control via radio frequency pulses. In this thesis, I will discuss my works on using nuclear spins to explore these areas. First, I will address our investigations of temporal correlations, quantified by the Leggett-Garg Inequality (LGI), of a qubit evolving under the superposition of unitary operators. Using a three-qubit quantum register, we experimentally realized superposed unitaries and demonstrated the violation of LGI beyond its maximal quantum value of 1.5, indicating enhanced non-classicality. Interestingly, we found that this superposed unitary dynamics improves robustness against decoherence. Next, I will discuss our work on Lee Yang (LY) zeros, points in the complex plane where the partition function goes to zero, which provide insights into a system’s thermodynamics and its behaviour near critical points. We propose a method to determine the full set of LY zeros of an asymmetric Ising system using a single quantum probe and demonstrate it experimentally with a three-qubit nuclear spin register. Interestingly, here also correlation plays an important role as the mutual information between the system and the quantum probe becomes maximum at the time points corresponding to LY zeros. Next, I will report our investigations of the quantum Mpemba effect in nuclear spin relaxation, which is an open system dynamics naturally occurring in nuclear spins at long times. We theoretically showed that a system far from steady state can relax faster than one nearer to equilibrium and demonstrated it experimentally. Finally, I will discuss my other work the localization and delocalization of entanglement due to local interactions, which causes and the apparent violation of quantum data processing inequality. Apart from experimentally realizing the respective dynamics using NMR methods, it was shown that the violation and corresponding non-complete positivity was only apparent by constructing a completely positive and trace-preserving map that describes the process.