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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Main Author: Aliakbarzadeh, Mojtaba
Format: Thesis
Language:English
English
Published: 2011
Subjects:
Online Access:http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf
http://psasir.upm.edu.my/id/eprint/26767/
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Institution: Universiti Putra Malaysia
Language: English
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spelling my.upm.eprints.267672022-01-26T05:35:09Z http://psasir.upm.edu.my/id/eprint/26767/ Generating mutually unbiased bases and discrete wigner function for three-qubit system 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 2011-05 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf Aliakbarzadeh, Mojtaba (2011) Generating mutually unbiased bases and discrete wigner function for three-qubit system. Masters thesis, Universiti Putra Malaysia. Wigner distribution Phase space (Statistical physics) Quantum computers English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
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
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
publishDate 2011
url http://psasir.upm.edu.my/id/eprint/26767/7/FS%202011%2083R.pdf
http://psasir.upm.edu.my/id/eprint/26767/
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