  Given a graph $G$ and a positive integer $d$, an orthogonal vector
$d$-coloring of $G$ is an assignment $f$ of vectors of $\mathbb{R}^d$ to $V(G)$
in such a way that adjacent vertices receive orthogonal vectors. The orthogonal
chromatic number of $G$, denoted by $\chi_v(G)$, is the minimum $d$ for which
$G$ admits an orthogonal vector $d$-coloring. This notion has close ties with
the notions of Lov\'asz Theta Function, quantum chromatic number, and many
other problems, and even though this and related metrics have been extensively
studied over the years, we have found that there is a gap in the knowledge
concerning the edge version of the problem. In this article, we discuss this
version and its relation with other insteresting known facts, and pose a
question about the orthogonal chromatic index of cubic graphs.
