Quantum Correlations: Geometry and Applications

Banerjee, Shreya (2021) Quantum Correlations: Geometry and Applications. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Shreya Banerjee (14IP016)) 14IP016.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

In the studies of quantum information and computation, the quantum correlations present in a non-classical system are seen as natural resources. In this thesis, we present a detailed study on quantification and characterization of multipartite quantum entanglement from a geometric perspective. Furthermore, we present protocols and algorithms where quantum correlations such as entanglement, quantum Fisher information, and quantum superposition have been used to provide advantages as well securities in quantum communication tasks, quantum speed-up, and protection against the decoherence in an open quantum system. The rapid progress in NISQ technologies have paved the way for designing powerful quantum algorithms which make use of the non-local correlations present in the quantum systems. An algorithm for hybrid sequencing of Deoxyribonucleic acid (DNA) is proposed using quantum tools. Using a modified version of Grover’s search algorithm, the perfect ordering of a spectrum of oligonucleotides is done to form an ideal spectrum. We further show that the algorithm is polynomial time as opposed to the most classical algorithms which are exponential-time, and also suggests an advantage of O(√n) over the polynomial-time classical hybrid DNA sequencing algorithm. An example of quantum hybrid DNA sequencing is provided as performed on IBM quantum experience.

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