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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.

Abstract / Synopsis

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’.

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Additional Metadata

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