Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z<sub>d</sub>

作     者：Semiu Oladipupo Oladejo Adediran Dauda Adeshola Adedayo David Adeniyi 

作者机构：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 

出 版 物：《Journal of Quantum Information Science》 (量子信息科学期刊（英文）)

年 卷 期：2019年第9卷第2期

页      面：111-121页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Lattice Join Meet Least Upper Bound (LUB) Greatest Lower Bound (GLB) Partially Ordered Set (POSET) 

摘      要：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 Zq) of a finite quantum system ∏(d)?with variables in Zd?and a finite system from the subsets of the set of divisors of d?is established.