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 (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.
Highlights
For quite some time, finite quantum systems with variables in d had received enormous attention [1] [2] [3] with special focus on mutually unbiased bases [4]-[9]
Join and meet algebraic structure which exists in non-near-linear finite geometry are discussed
We focus our attention on the structure of lattice found in lines in non-near-linear finite geometry and Hilbert space of finite quantum systems
Summary
Finite quantum systems with variables in d had received enormous attention [1] [2] [3] with special focus on mutually unbiased bases [4]-[9]. The weak mutually unbiased base ( WMUB ) is getting more interest from researchers [10] [11] This might be due to the fact that they are concepts that have a significant role in quantum computation and information [12] [13] [14] [15]. Most work done on finite geometry is on near-linear geometry We focus our attention on the structure of lattice found in lines in non-near-linear finite geometry and Hilbert space of finite quantum systems.
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