  In quantum private information retrieval (QPIR), a user retrieves a classical
file from multiple servers by downloading quantum systems without revealing the
identity of the file. The QPIR capacity is the maximal achievable ratio of the
retrieved file size to the total download size. In this paper, the capacity of
QPIR from MDS-coded and colluding servers is studied for the first time. Two
general classes of QPIR, called stabilizer QPIR and dimension-squared QPIR
induced from classical strongly linear PIR are defined, and the related QPIR
capacities are derived. For the non-colluding case, the general QPIR capacity
is derived when the number of files goes to infinity. A general statement on
the converse bound for QPIR with coded and colluding servers is derived showing
that the capacities of stabilizer QPIR and dimension-squared QPIR induced from
any class of PIR are upper bounded by twice the classical capacity of the
respective PIR class. The proposed capacity-achieving scheme combines the
star-product scheme by Freij-Hollanti et al. and the stabilizer QPIR scheme by
Song et al. by employing (weakly) self-dual Reed--Solomon codes.
