Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Entanglement and Topological Phenomena in Quantum Walks(01. Izmir Institute of Technology, 2023) Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyQuantum walk, a counterpart of classical random walk, is widely used in the development of quantum algorithms and the modelling of physical systems. Since it has a simple and powerful mathematical structure, its implementation in physical systems serves to solve complex problems. In one-dimensional space, we investigated the topological properties of the simple quantum walk, and under which conditions the simple quantum walk possesses winding numbers. Then, we introduced the split-step quantum walk in a twodimensional space and numerically obtained Chern number phase diagram of each band as a function of rotation parameters. Subsequently, we introduced and studied the quantum walk protocols governed by two coins in a two-dimensional space. We first explored the entanglement and topological properties of a quantum walk protocol governed by a single non-local two-coin operator followed by translations along two spatial directions each governed by a different coin. We deduced that the motion reduces to one-dimensional motion in two spatial directions in decoupled coin subspaces. Then, we studied the split-step quantum walk protocols, where each step is comprised of local coin operations, followed by translations, non-local coin operations, and translations again. In these protocols, each step involves two translations along two spatial directions, and translations along a given spatial direction were either governed by the same coin or alternating coins. We also explored three different non-local coin operations, where a collective rotation takes place in a coin space conditioned on the state of the other coin's state along the same direction or perpendicular direction. We identified the effective Hamiltonian of the system and determined its eigenstates which are comprised of four bands in the Brillouin zone. For all the protocols we have introduced, we studied the coin-coin entanglement and topological properties as a function of coin rotation parameters.Master Thesis Quantum Walks: Entanglement Between Spatial Degrees of Freedom and Interference in Multi-Photon Walks(Izmir Institute of Technology, 2020) Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyQuantum walks can be described as quantum analogues of classical random walks. In quantum walks, the direction of the walker is dictated by the quantum state of a coin in a coherent fashion. Unlike classical random walk with a fair coin, quantum walk has non-Markovian property. First, we studied 2-D quantum walk analytically and numerically with one-walker and two entangled coins to investigate the transfer of the entanglement in initial coins state to spatial degrees of freedom. The coins are Hadamard Coin, Fourier Coin, among which the Fourier coin generates entanglement, thus increase entanglement between spatial degrees of freedom. Here we calculated the amount of entanglement using negativity. In the second part we studied average photon number correlations for 1-D quantum walk with many body bosonic walkers, like different light sources, to investigate quantum interference effects and we showed the second-order intensity correlations function in terms of the probability amplitudes of the 1-D quantum walk with Hadamard coin. We compared the resulting correlations for various initial many photon states.