Tractable measure of nonclassical correlation using density matrix truncations

In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of this paradigm, we propose a measure of nonclassical correlation by using truncations of a density matrix down to individual eigenspaces. It is computable within polynomial time in the dimension of the Hilbert space albeit imperfect in the detection range. This is in contrast to the measures conventionally used for the paradigm. The computational complexity and mathematical properties of the proposed measure are investigated in detail and the physical picture of its definition is discussed.Comment: 10 pages, 2 figures, v2: minor revision, a figure replaced, v3: minor revision, an inseparable state for which M vanishes was corrected, more accurate complexity was given, v4: minor revision, counterexamples to additivity properties were given, v5: minor revision, definition of M and discussions improved, v6: major revision with an improved definition of M, to appear in QI

Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor

This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and counter-intuitive, is one of the main type considered in this thesis. Quantum correlations play a major role in achieving, the much talked, computational speedup. Creation and detection of such correlations experimentally is a major thrust area in experimental quantum information processing field. Main goals of the studies undertaken in this thesis were to come up with strategies to detect the entanglement in a 'state-independent' way and with low experimental resources. The core of all the detection protocols is based on our own developed method which enables us to measure any observable with high accuracy. The experimental protocol has been successfully implemented to detect the entanglement of random two-qubit pure states. Further, the schemes for the experimental detection as well as classification of generic and general three-qubit pure states have also been devised and implemented successfully. Quantum correlation possessed by mixed and$/$or separable states e.g. non-classical, bound-entanglement and of non-local nature were also investigated. In all the investigations, the results were verified by one or more alternative ways e.g. full quantum state tomography.Comment: PhD Thesis, Indian Institute of Science Education and Research Mohali (2019), 143 pages, 26 figures, 9 tables, 7 chapter