  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 the sense that a smaller $t$ would not improve the retrieval
rate. In this paper, the QPIR setting is extended to allow for retrieval with
high rate for any number of colluding servers $t$ with $1 \leq t \leq n-k$.
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.
