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The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field

Generally, quantum states are abstract states that carry probabilistic information of position and momentum of any dynamical physical quantity in quantum system. E.P.Wigner (1932) had introduced a function that can determine the combination of position and momentum simultaneously, and it was the...

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Main Author: Zainy, Mazlinda
Format: Thesis
Language:English
English
Published: 2009
Subjects:
Electrons
Phase space (Statistical physics)
Galois theory
Online Access:http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf
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spelling oai:psasir.upm.edu.my:11974 http://psasir.upm.edu.my/id/eprint/11974/ The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field Zainy, Mazlinda Generally, quantum states are abstract states that carry probabilistic information of position and momentum of any dynamical physical quantity in quantum system. E.P.Wigner (1932) had introduced a function that can determine the combination of position and momentum simultaneously, and it was the starting point to define a phase space probability distribution for a quantum mechanical system using density matrix formalism. This function named as Wigner Function. Recently, Wootters (1987) has developed a discrete phase space analogous to Wigner’s ideas. The space is based on Galois field or finite field. The geometry of the space is represented by N ´ N point, where N denoted the number of elements in the field and it must be a prime or a power of a prime numbers. In this work, we study the simplest way to compute the binary operations in finite field in order to form such a discrete space. We developed a program using Mathematica software to solve the binary operation in the finite field for the case of 3-qubit and 2-qutrit systems. The program developed should also be extendible for the higher number of qubit and qutrit. Each state is defined by a line aq + bp = c and parallel lines give equivalent states. The results show that, there are 9 set of parallel lines for the 3-qubit system and 10 sets of parallel lines for 2-qutrit system. These complete set of parallel lines called a ‘striation’. 2009-11 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf Zainy, Mazlinda (2009) The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field. Masters thesis, Universiti Putra Malaysia. Electrons Phase space (Statistical physics) Galois theory English
institution UPM IR
collection UPM IR
language English
English
topic Electrons
Phase space (Statistical physics)
Galois theory
spellingShingle Electrons
Phase space (Statistical physics)
Galois theory
Zainy, Mazlinda
The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
description Generally, quantum states are abstract states that carry probabilistic information of position and momentum of any dynamical physical quantity in quantum system. E.P.Wigner (1932) had introduced a function that can determine the combination of position and momentum simultaneously, and it was the starting point to define a phase space probability distribution for a quantum mechanical system using density matrix formalism. This function named as Wigner Function. Recently, Wootters (1987) has developed a discrete phase space analogous to Wigner’s ideas. The space is based on Galois field or finite field. The geometry of the space is represented by N ´ N point, where N denoted the number of elements in the field and it must be a prime or a power of a prime numbers. In this work, we study the simplest way to compute the binary operations in finite field in order to form such a discrete space. We developed a program using Mathematica software to solve the binary operation in the finite field for the case of 3-qubit and 2-qutrit systems. The program developed should also be extendible for the higher number of qubit and qutrit. Each state is defined by a line aq + bp = c and parallel lines give equivalent states. The results show that, there are 9 set of parallel lines for the 3-qubit system and 10 sets of parallel lines for 2-qutrit system. These complete set of parallel lines called a ‘striation’.
format Thesis
author Zainy, Mazlinda
author_facet Zainy, Mazlinda
author_sort Zainy, Mazlinda
title The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
title_short The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
title_full The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
title_fullStr The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
title_full_unstemmed The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field
title_sort discrete phase space for 3-qubit and 2-qutrit systems based on galois field
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf
_version_ 1782718338575630336
score 12.935284

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