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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
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Γρατσέα, Αικατερίνη Σ.
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Thesis advisor
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Lewenstein, Maciej
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Reviewer
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Τομαράς, Θεόδωρος
Λαμπρόπουλος, Παναγιώτης
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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.
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Language |
English |
Subject |
Entanglement |
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Quantum information |
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Quantum optics |
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Καταστάσεις μεγάλων διαστάσεων |
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Κβαντική οπτική |
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Κβαντική πληροφορία |
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Κβαντική συσχέτιση |
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Κβαντικός περίπατος |
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Φωτόνιο |
Issue date |
2018-11-23 |
Collection
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School/Department--School of Sciences and Engineering--Department of Physics--Post-graduate theses
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Type of Work--Post-graduate theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/8/9/e/metadata-dlib-1541578051-151435-29910.tkl
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Views |
441 |