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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| Online Access: | http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf |
| _version_ | 1825944967388856320 |
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| author | Zainy, Mazlinda |
| author_facet | Zainy, Mazlinda |
| author_sort | Zainy, Mazlinda |
| collection | UPM |
| 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’. |
| first_indexed | 2024-03-06T07:24:11Z |
| format | Thesis |
| id | upm.eprints-11974 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:24:11Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | upm.eprints-119742013-05-27T07:50:32Z 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 |
| 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 |
| title | 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_short | 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 |
| topic | Electrons Phase space (Statistical physics) Galois theory |
| url | http://psasir.upm.edu.my/id/eprint/11974/1/FS_2009_39_A.pdf |
| work_keys_str_mv | AT zainymazlinda thediscretephasespacefor3qubitand2qutritsystemsbasedongaloisfield AT zainymazlinda discretephasespacefor3qubitand2qutritsystemsbasedongaloisfield |