Estudo de Emaranhamento Quântico em Estados Hipergrafo

Abstract

In this thesis, we introduce and analyze the entanglement properties of randomized hypergraph states, as an extended notion of the randomization procedure in the quantum logic gates for the usual graph states, recently proposed in the literature. Here, the probabilities of applying an imperfect generalized controlled gate simulates the noisy operations over the qubits. For the mixed multiqubit state class, we obtain entanglement measures such as concurrency, negativity and multiparty entanglement. Different states are analyzed, including the symmetric hypergraph for up to five qubits. The presence of multipartite entanglement is analyzed in detail with emphasis on the unprecedented observation of sudden death of entanglement (SDE) and rebirth of entanglement for the randomized states considering hyperedges of different orders, emphasizing the new behavior that emerges for non-uniform entangled states, generating a kind of competition for entanglement as a resource, facilitating the understanding of the behavior of states under realistic noise conditions in the laboratory. Furthermore, we present a concise introduction to Gaussian quantum information and its applicability to Gaussian graph states and hypergraph states.