The present work aims to exploit the interplay between algebraic properties of rings and graph-theoretic structures some associated graphs. We introduce commutatively closed graphs investigate subsets a ring with help graph theory. In particular, we compute diameter matrix Artinian semisimple algebras.

Quantum state tomography (QST) aims at estimating a quantum from averaged measurements made on copies of that state. Most algorithms rely QST some point and it is well-explored topic in the literature, mostly for mixed states. In this paper we focus pure using parallel unentangled measurements. Pure states are small but useful subset all states, their requires fewer essentially phase recovery p...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.