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

• 作者: Adedayo David Adeniyi Adediran Dauda Adeshola Semiu Oladipupo Oladejo
• 来源期刊: 量子信息科学期刊(英文)
• 学科: 数学
• 关键词: Lattice Join Meet Least Upper BOUND (LUB) GREATEST Lower BOUND (GLB) Partially Ordered Set (POSET)
• 年，卷（期）: 2019,（2）
• 页码范围: 111-121
• 页数: 11页
• 分类号: O1

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.