arXiv:2608.00265v1 Announce Type: new Abstract: We study the problem of testing low-degree phase states, namely m-qudit quantum states of the form $q^{-m/2} \sum_{x \in \mathbb{F}_q^m} \omega^{f(x)} |x>$, where $f$ is a degree-$d$ polynomial. In contrast to the classical setting, where low-degre