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Identifier 000419053
Title Preparation of high-dimensional maximally entangled states of a single photon in a quantum walk
Alternative Title Προετοιμασία σύμπλεκτων καταστάσεων μέγιστης συσχέτισης και μεγάλων διαστάσεων ενός φωτονίου με κβαντικούς περιπάτους
Author Γρατσέα, Αικατερίνη Σ.
Thesis advisor Lewenstein, Maciej
Reviewer Τομαράς, Θεόδωρος
Λαμπρόπουλος, Παναγιώτης
Abstract Quantum information theory has greatly evolved in recent years and offers advancements in many different fields, among them quantum walks (QWs). Α quantum walk consists of n discrete rotations (coin operators) and fixed translations (shift operators). This thesis aims to propose an algorithm for the preparation of high-dimensional maximally entangled states of a single photon with quantum walks. Entanglement is a vital resource in quantum information and computation for transfering information around; and recently single-photon entanglement has become an active research field. We should emphasize that entanglement in a single-photon occurs between the different degrees of freedom of the particle, i.e. polarization, orbital angular momentum, time-bin energy and spatial mode. There are many measurements related to entanglement but we will restrict the work to the Schmidt norms; we bipartite the system to two subsystems and measure the correlations between them. This measurement, as it is proven in detail, is related to the Renyi α entropy. In this work, we explore the preparation of single-photon maximally entangled states with respect to the aforementioned definition of the entanglement, the Schimdt norm. The bipartition of the system is between the spin and orbital angular momentum (OAM) degrees of freedom. Additionally, we exploit the large size of the (OAM) Hilbert space to construct high-dimensional maximally entangled states, which has been gaining increasing interest in the quantum information technologies in the recent years. Specifically, we use QWs with different coin operators at each step because these quantum walks enhance the value of entanglement at the final state. We propose two different methods to construct the aforementioned states. The first one merges two already existing algorithms to generate maximally entangled states: an algorithm that finds a maximally entangled state with the aforementioned definition and an algorithm that finds the required coin operators for the construction of a desired state with a quantum walk. The second approach aims to transform the above problem to an optimization problem. The algorithm starts with an arbitrary initial state and, by using optimization techniques such as stochastic gradient descent, the free coin parameters of the quantum walk are determined so that the output state to be a maximally entangled state. It is shown that the second method is more advantageous, since it has a direct experimental implementation and also allows for the consideration of experimental imprefections. Significantly, contrary to other related works the number of optical elements scale linearly with the size of the system.
Language English
Subject Entanglement
Quantum information
Quantum optics
Καταστάσεις μεγάλων διαστάσεων
Κβαντική οπτική
Κβαντική πληροφορία
Κβαντική συσχέτιση
Κβαντικός περίπατος
Φωτόνιο
Issue date 2018-11-23
Collection   School/Department--School of Sciences and Engineering--Department of Physics--Post-graduate theses
  Type of Work--Post-graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/8/9/e/metadata-dlib-1541578051-151435-29910.tkl Bookmark and Share
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