Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z_d
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Date
2019-05-01
Journal Title
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Publisher
Scientific Research Publishing
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 d2
were expressed as products of lines in near-linear finite geometry 2
p (where
p is a prime). An existence of lattice between any pair of near-linear finite
geometry 2 ,( = 1,, ) pj j k of d2 is confirmed. For q | d , a one-to-one correspondence
between the set of subgeometry 2
qj of d2 and finite geometry
2 d from the subsets of the set {(d)} of divisors of d (where each divisor
represents a finite geometry) and set of subsystems {Π(q)} (with variables
in q ) of a finite quantum system Π(d) with variables in d and a finite
system from the subsets of the set of divisors of d is established.
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Citation
http://www.scirp.org/journal/jqis