TITLE:
Lattice Theory for Finite Dimensional Hilbert Space with Variables in Zd
AUTHORS:
Semiu Oladipupo Oladejo, Adediran Dauda Adeshola, Adedayo David Adeniyi
KEYWORDS:
Lattice, Join, Meet, Least Upper Bound (LUB), Greatest Lower Bound (GLB), Partially Ordered Set (POSET)
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.9 No.2,
April
18,
2019
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 (wherepis 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 Zq) of a finite quantum system ∏(d)with variables in Zdand a finite system
from the subsets of the set of divisors of dis established.