Generating mutually unbiased bases and discrete wigner function for three-qubit system

In this research, we construct Wigner functions on discrete phase spaces to represent quantum states for the special case of 3-qubit system. For determining this discrete phase space, we label the axes of phase space with finite field (Galois field) having eight elements. Based on this labeling, we...

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主要作者:	Aliakbarzadeh, Mojtaba
格式:	Thesis
语言:	English English
出版:	2011
主题:	Wigner distribution Phase space (Statistical physics) Quantum computers
在线阅读:	http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf
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spelling	my-upm-ir.267672022-01-26T05:35:09Z Generating mutually unbiased bases and discrete wigner function for three-qubit system 2011-05 Aliakbarzadeh, Mojtaba In this research, we construct Wigner functions on discrete phase spaces to represent quantum states for the special case of 3-qubit system. For determining this discrete phase space, we label the axes of phase space with finite field (Galois field) having eight elements. Based on this labeling, we developed a program in Matlab software for 3-qubit system which is also extendible for higher dimensions and more number of cubits. Results of this program lead to nine sets of parallel lines which is named as striations. Equivalently we label the horizontal and vertical axes of our phase space by quantum states of 3 cubits. This labeling and the use of suitable translation vectors on our striations produce the nine mutually unbiased bases for the Hilbert space. For calculating discrete Wigner function, we have determined appropriate quantum net Q(¸). There are 89 different choices for defining quantum nets but by using some unitary operators we reduce our choices to just eight different choices of quantum nets (eight similarity classes). We developed another program in Maple, which gives us eight different similarity classes of quantum nets. This program also gives us the phase-space point operators A® related to each class of quantum nets (these A® operators are used in calculating Wigner function). Based on one of these similarity classes, we calculated the Wigner functions for GHZ and W states and also an embedded Bell state which is not completely entangled. We discussed some of the properties of these Wigner functions Wigner distribution Phase space (Statistical physics) Quantum computers 2011-05 Thesis http://psasir.upm.edu.my/id/eprint/26767/ http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf application/pdf en public masters Universiti Putra Malaysia Wigner distribution Phase space (Statistical physics) Quantum computers Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Wigner distribution Phase space (Statistical physics) Quantum computers
spellingShingle	Wigner distribution Phase space (Statistical physics) Quantum computers Aliakbarzadeh, Mojtaba Generating mutually unbiased bases and discrete wigner function for three-qubit system
description	In this research, we construct Wigner functions on discrete phase spaces to represent quantum states for the special case of 3-qubit system. For determining this discrete phase space, we label the axes of phase space with finite field (Galois field) having eight elements. Based on this labeling, we developed a program in Matlab software for 3-qubit system which is also extendible for higher dimensions and more number of cubits. Results of this program lead to nine sets of parallel lines which is named as striations. Equivalently we label the horizontal and vertical axes of our phase space by quantum states of 3 cubits. This labeling and the use of suitable translation vectors on our striations produce the nine mutually unbiased bases for the Hilbert space. For calculating discrete Wigner function, we have determined appropriate quantum net Q(¸). There are 89 different choices for defining quantum nets but by using some unitary operators we reduce our choices to just eight different choices of quantum nets (eight similarity classes). We developed another program in Maple, which gives us eight different similarity classes of quantum nets. This program also gives us the phase-space point operators A® related to each class of quantum nets (these A® operators are used in calculating Wigner function). Based on one of these similarity classes, we calculated the Wigner functions for GHZ and W states and also an embedded Bell state which is not completely entangled. We discussed some of the properties of these Wigner functions
format	Thesis
qualification_level	Master's degree
author	Aliakbarzadeh, Mojtaba
author_facet	Aliakbarzadeh, Mojtaba
author_sort	Aliakbarzadeh, Mojtaba
title	Generating mutually unbiased bases and discrete wigner function for three-qubit system
title_short	Generating mutually unbiased bases and discrete wigner function for three-qubit system
title_full	Generating mutually unbiased bases and discrete wigner function for three-qubit system
title_fullStr	Generating mutually unbiased bases and discrete wigner function for three-qubit system
title_full_unstemmed	Generating mutually unbiased bases and discrete wigner function for three-qubit system
title_sort	generating mutually unbiased bases and discrete wigner function for three-qubit system
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf
_version_	1747811559749451776

Generating mutually unbiased bases and discrete wigner function for three-qubit system

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