For a simple graph $Γ$ , a (bipartite)tree-line graph and a tree-graph of $Γ$ can be defined. With a (bipartite)tree-line graph constructed by the function $(b)\ell$ , we study the continuous quantum walk on $(b)\ell ^n Γ$ . An equitable partition of a bipartite tree-line graph is obtained by its corresponding derived tree graph. This paper also examines quantum walks on derived graphs, whose vertices represent their basis state.For a simple graph $Γ$, a (bipartite)tree-line graph and a tree-graph of $Γ$ can be defined. With a (bipartite)tree-line graph constructed by the function $(b)\ell$, we study the continuous quantum walk on $(b)\ell ^n Γ$. An equitable partition of a bipartite tree-line graph is obtained by its corresponding derived tree graph. This paper also examines quantum walks on derived graphs, whose vertices represent their basis state.

arXiv:2504.13000Apr 17, 20250 citations

A Combinatorial Approach to Nonlocality and Contextuality

Anthony Leverrier

Feb 25, 20130 citations

On geometrical aspects of the graph approach to contextuality

Bárbara Amaral, Marcelo Terra Cunha

The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph theory, leading to a beautiful geometric characterization of such sets. This geometry can also be explored in the definition of contextuality quantifiers based on geometric distances, which is important for the resource theory of contextuality, developed after the recognition of contextuality as a potential resource for quantum computation. In this paper we review the geometric aspects of contextuality and use it to define several quantifiers, which have the advantage of being applicable to the exclusivity approach to contextuality, where previously defined quantifiers do not fit.The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph theory, leading to a beautiful geometric characterization of such sets. This geometry can also be explored in the definition of contextuality quantifiers based on geometric distances, which is important for the resource theory of contextuality, developed after the recognition of contextuality as a potential resource for quantum computation. In this paper we review the geometric aspects of contextuality and use it to define several quantifiers, which have the advantage of being applicable to the exclusivity approach to contextuality, where previously defined quantifiers do not fit.

arXiv:1709.04812Sep 14, 20175 citations

For a simple graph

Γ

, a (bipartite)tree-line graph and a tree-graph of

Γ

can be defined. With a (bipartite)tree-line graph constructed by the function

(b)\ell

, we study the continuous quantum walk on

(b)\ell ^n Γ

. An equitable partition of a bipartite tree-line graph is obtained by its corresponding derived tree graph. This paper also examines quantum walks on derived graphs, whose vertices represent their basis state.