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Lattice Theory for Finite Dimensional Hilbert Space with Variables in Zd

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Document pages: 11 pages

Abstract: Inthis work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines innon-near-linear finite geometry  were expressed as products of lines in near-linearfinite geometry  (where p is a prime). Anexistence of lattice between any pair of near-linear finite geometry  of  is confirmed. For q|d, a one-to-one correspondencebetween the set of subgeometry  of  and finite geometry  from the subsets ofthe set {D(d)} of divisors of d (where each divisor represents a finitegeometry) and set of subsystems {∏(q)} (with variables in Zq) of a finite quantum system ∏(d) with variables in Zd and a finite systemfrom the subsets of the set of divisors of d is established.

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