A note on weight systems which are quantum states

A result of Corfield, Sati, and Schreiber asserts that ${\mathfrak{g}\mathfrak{l}}_n$-weight systems associated to the defining representation are quantum states. In this short note we extend this result to all ${\mathfrak{g}\mathfrak{l}}_n$-weight systems corresponding to labeling by symmetric and exterior powers of the defining representation.