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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| Format: | Thesis |
| Language: | English English |
| Published: |
2009
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf |
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| Summary: | 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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