IIIT Hyderabad Publications
On Bell Nonlocality and Quantum Correlations
Author: Palash Pandya
Report no: IIIT/TH/2016/63
Advisor:Indranil Chakrabarty,Harjinder Singh
After Bell’s celebrated work in 1964, demonstrating the incompatibility of Quantum Mechanics with the notion of local realism, there have been numerous conceptual and technical developments for studying nonlocality in quantum systems. The Bell inequality and Bell-type inequalities, set an upper bound on the correlations between measurement statistics of many particle systems that cannot be explained by local hidden variable models. Quantum entanglement has proven to be a key resource for various information theoretic protocols such as dense coding, teleportation, etc. Their numerous applications makes it consequential to pinpoint their behaviour. In the first chapter, a cursory delineation of the historical events in the development of Quantum theory, is followed by a concise introduction to the theory and mathematical tools needed for this thesis. The landmark papers of EPR and John Bell are discussed, so as to provide an understanding of the significance of Bell’s theorem and thus the Bell’s inequalities. Quantum Entanglement is discussed, and in particular, measures that are used later to quantify tripartite correlations are described in greater detail. The second chapter discusses Bell-CHSH inequality for two qubit systems and Bell-type inequalities for multi-qubit systems; and the theory independent derivation of Bell-CHSH inequality, known as the Device Independent scenario, where the characteristics of the probability distributions shared between two or more parties are sufficient to define different kinds of nonlocal correlations, without recourse to any underlying theory. The third chapter briefly goes over the disjoint sets of genuinely entangled three qubit pure states that constitute the GHZ and W classes of states. It also introduces a new class of states called the Maximally Bell-Inequality Violating (MBV) class of states. This is followed by the description of the analytical calculations for the maximum bipartite Bell Inequality violations of the three classes. For each of the three classes a complementary relation is then established between the maximum bipartite Bell Inequality Violation and tripartite correlation measures - Generalized Geometric Measure (GGM), Tangle and Discord Monogamy Score (DMS). Numerical evidence for this is also provided. The fourth chapter discusses first the convex roof extension of the complementary relations described above and then it goes on to discuss the results of the obvious next step, comparing tripartite nonlocality with tripartite correlation measures. The analysis is put forth as a future problem which possibly has quite a few fascinating insights in store.
Full thesis: pdf
Centre for Security, Theory and Algorithms
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