  In the classical private information retrieval (PIR) setup, a user wants to
retrieve a file from a database or a distributed storage system (DSS) without
revealing the file identity to the servers holding the data. In the quantum PIR
(QPIR) setting, a user privately retrieves a classical file by receiving
quantum information from the servers. The QPIR problem has been treated by Song
et al. in the case of replicated servers, both with and without collusion. QPIR
over $[n,k]$ maximum distance separable (MDS) coded servers was recently
considered by Allaix et al., but the collusion was essentially restricted to
$t=n-k$ servers. In this paper, the QPIR setting is extended to account for
more flexible collusion of servers satisfying $t < n-k+1$. Similarly to the
previous cases, the rates achieved are better than those known or conjectured
in the classical counterparts, as well as those of the previously proposed
coded and colluding QPIR schemes. This is enabled by considering the stabilizer
formalism and weakly self-dual generalized Reed--Solomon (GRS) star product
codes.
