Experimental Characterization and Detection of Quantum Entanglement and Nonclassical Correlations

Abstract

The thesis explores various facets of quantum information processing, primarily fo cusing on entanglement detection, quantification, and characterization. It also touches upon broader aspects of quantum correlations, including discord. Experimental imple mentations of these concepts are conducted on spin ensemble based nuclear magnetic resonance (NMR) and superconductor-based IBM quantum processors, highlighting their practical applicability in quantum information science. Quantum entanglement is a critical factor driving advancements in quantum technologies. However, detecting this fundamental property is generally considered to be an NP-hard problem. Tra ditional methods such as tomography are not feasible due to their resource-intensive nature. Moreover, many theoretical methods for entanglement detection are not ex perimentally friendly, posing significant challenges in practical implementation. In three-qubit systems, SLOCC (Stochastic Local Operations with Classical Communi cation) classification categorizes quantum states based on their equivalence under local operations and classical communication. This classification scheme identifies different classes of entanglement that remain invariant under such operations, providing insights into the multipartite entanglement structure of quantum states. Specifically, for three qubits, there are 6 distinct SLOCC classes. Several protocols are proposed and experi mentally verified for the SLOCC classification and detection of genuinely multipartite entanglement (GME) in both three-qubit pure and mixed quantum states. The thesis begins with the presentation of a novel protocol for classifying three qubit pure states into SLOCC entanglement classes using the reconstruction of corre lation tensors on an NMR quantum computer. This protocol requires the measurement of 13 operators, where the expectation values of these operators form the elements of these tensors. These same expectation values are used to construct a concurrence func tion, which quantifies the global entanglement present in the system. Building on this vii 0. Abstract foundation, an artificial neural network (ANN) model is developed to detect genuinely multipartite entanglement (GME) and classify three-qubit states under SLOCC. It has been demonstrated that 6 features are sufficient for SLOCC classification and 4 features for GME classification when states are expressed in the canonical basis. Additionally, the thesis explores the generation and detection of entanglement in three-qubit PPT en tangled GHZ diagonal states using both linear and nonlinear entanglement witnesses. Implementation on IBM hardware demonstrates the advantage of nonlinear witnesses in NISQ devices. It introduces an algorithm for classifying 3 and 4 qubit systems us ing matrix product states (MPS) into SLOCC classes using MPS properties. The work also extends to the measurement of quantum discord, a form of quantum correlation that goes beyond entanglement. Experimental techniques are developed for quantify ing discord in NMRsystems, enhancing the understanding of quantum correlations and their implications for quantum information processing. The thesis further explores the dynamics of quantum systems, distinguishing between Markovian and non-Markovian behavior using convex combinations of Pauli semigroups, with experimental valida tion on NMRquantumprocessor.