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Detecting Genuine Multipartite Quantum Entanglement with eternal non-MarkovianityAuthor: Ankit Shambhunath Vaishy 20161020 Date: 2022-12-06 Report no: IIIT/TH/2022/155 Advisor:Subhadip Mitra,Samyadeb Bhattacharya AbstractThe study of quantum entanglement is significant for the development of Quantum Information science. Hence its detection becomes very vital. Detection of quantum entanglement is an NP-hard problem, and this is why we don’t have a generalized solution for the detection of quantum entanglement. There are many ways to detect quantum entanglement, but our study will mainly focus on detecting entanglement using the mathematical theory of positive but not completely positive maps. Positive but not completely positive maps applied to a subsystem of a bipartite quantum state are a central tool in characterizing entanglement in a bipartite system. In this study, we utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map. In the multipartite case, the direct application of a positive but not completely positive map does not work. It fails to capture the distinction among different classes of multipartite entanglement. We thus generalise this bipartite concept to the multipartite setting by introducing a special non-positive maps that are positive on the subset of bi-separable states, but can map to a non-positive element if applied to a genuine multipartite entangled state. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity. Full thesis: pdf Centre for Security, Theory and Algorithms |
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