Geometric Measure of Genuine Multipartite Entanglement

Kumar, Abhishek (2022) Geometric Measure of Genuine Multipartite Entanglement. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Abhishek Kumar (17MS118)) 17MS118_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (654kB)

Abstract

Entanglement, which arises from the superposition principle and the tensor product structure of multipartite quantum systems, is one of the most counter-intuitive phenomenons, and has played a central role in the quantum information revolution. Since it is a key resource in most quantum information processing tasks, characterising and quantifying entanglement in the multiparty system has attracted a significant attention in the past two decades. In particular, genuine multipartite entanglement, i.e., when none of the parties are separable is of interest when a task requires correlation among three or more parties. An intuitive and elegant geometrical approach to quantify genuine multipartite entanglement for pure three party systems was very recently put forward by Xie and Eberly. In this project, we extend this geometrical approach to the four party system, and argue that the entanglement structure is still planar, in contrast to what was suggested in the above work. We obtain several constraints for the bipartite concurrences and provide a geometrical measure of GME. This work we believe is a step forward in understanding the complex structure of multiparty entanglement.

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