Experimental studies of quantum contextuality and non locality on an NMR quantum information processor

Abstract

This thesis focuses on the experimental study of foundational concepts of quantum theory such as quantum contextuality, and nonlocality on an nuclear magnetic reso- nance (NMR) quantum information processor. Contextuality and nonlocality are cru- cial aspects of quantum mechanics, and their existence demonstrates the fundamental departure from the classical theories such as hidden variable theories. Nonlocality and quantum contextuality can be revealed via a violation of non-contextual inequalities such as the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality and Bell-type in- equalities such as the Clauser-Horne-Shimony-Holt (CHSH) inequality, respectively. These fundamental ideas have emerged as a crucial tool for enhancing computation and establishing secure quantum communications. Monogamy relationships can be used to examine quantum contextuality and nonlocality simultaneously. Numerous quan- tum information tasks, such as secure communication, self-testing, and randomness certification, have found extensive use for monogamy of correlations. One of the major areas of focus in experimental quantum computing is the experi- mental study of the above quantum correlations. This thesis aims to conduct an exper- imental study of quantum contextual correlations, nonlocal correlations, and monog- amous relationships of these quantum correlations on an NMR quantum information processor. Different types of experimental schemes, suitable for the NMR experimen- tal set-up, have been developed that enable the precise measurement of the relevant observables. Experimental demonstration of fully contextual quantum correlations has been successfully experimentally demonstrated on two-qubit and three-qubit states. A generalized quantum scattering circuit is presented which can be used to perform a non-invasive measurement. Further, Peres-Mermin (PM) inequality is successfully experimentally demonstrated on a three-qubit system. The monogamy relationship be- tween contextuality and nonlocality has been successfully demonstrated on a ququart- qubit system using three NMR qubits. The theoretical protocol has also been developed to evaluate monogamy relationships of entropic non-contextuality (ENC) inequalities, and the theoretical results have been verified experimentally. Finally, experimental im- plementation of variational quantum algorithms is employed to predict the molecular ground-state energy of the H 2 molecule.