An existence condition for multilinear quantum operations
Recall that a quantum variable is a variable \(x\), with which an element \(g_x\) of a fixed abelian group \(G\) and a character \(\chi^ x: G \rightarrow k^*\) are associated. In this paper the author shows that there exists a non-zero multilinear quantum operation in a set of quantum variables \(x_1, x_2, \cdots , x_n\) if and only if this set is conforming, i.e., \[ \prod_{1\leq i\neq j\leq n}\chi^{x_i}(g_{x_j})=1. \] Moreover, he proves that if the set \(x_1, x_2, \cdots , x_n\) has no proper conforming subset, then the dimension of the space of all multilinear quantum operation in \(x_1, x_2, \cdots , x_n\) equals \((n-2)!\).
scientific article; zbMATH DE number 1340610
scientific article