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Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z<sub>d</sub>
Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
Department of Statistical and Mathematical Science, College of Pure and Applied Science, Kwara State University, Ilorin, Nigeria
Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
- 1 Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
- 2 Department of Statistical and Mathematical Science, College of Pure and Applied Science, Kwara State University, Ilorin, Nigeria
- 3 Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria
Journal of Quantum Information Science·Volume 09 (2019)·Pages 111–121·Published 18 April 2019·DOI10.4236/jqis.2019.92006
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Abstract
In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry were expressed as products of lines in near-linear finite geometry (where p is a prime). An existence of lattice between any pair of near-linear finite geometry of is confirmed. For q|d , a one-to-one correspondence between the set of subgeometry of and finite geometry from the subsets of the set {D(d)} of divisors of d (where each divisor represents a finite geometry) and set of subsystems {∏(q)} (with variables in Z<SUB>q</SUB> ) of a finite quantum system ∏(d) with variables in Z<SUB>d</SUB> and a finite system from the subsets of the set of divisors of d is established.
KeywordsLatticeJoinMeetLeast Upper Bound (LUB)Greatest Lower Bound (GLB)Partially Ordered Set (POSET)
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