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

Zainy, Mazlinda (2009) The Discrete Phase Space For 3-Qubit And 2-Qutrit Systems Based On Galois Field. Masters thesis, Universiti Putra Malaysia.

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Abstract

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’.

Item Type:Thesis (Masters)
Subject:Electrons
Subject:Phase space (Statistical physics)
Subject:Galois theory
Chairman Supervisor:Hishamuddin B. Zainuddin, PhD
Call Number:FS 2009 39
Faculty or Institute:Faculty of Science
ID Code:11974
Deposited By: Mohd Nezeri Mohamad
Deposited On:19 Jul 2011 10:05
Last Modified:27 May 2013 15:50

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