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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. Partial results have been published at ISIT 2021 [1]. C. Hollanti and M.

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. Two 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. The capacities of symmetric and non-symmetric QPIR with coded and colluding servers are proved to coincide, being double to their classical counterparts. 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. I. INTRODUCTIONWith the amount of data stored in distributed storage systems steadily increasing, the demand for user privacy has surged in recent years. One notion that has received considerable attention is private information retrieval (PIR), where the Partial results have been accepted to ISIT 2021 [1]. C. Hollanti and M.

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This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. In this work, a flexible and robust private information retrieval (PIR) scheme based on binary non-maximum distance separable (non-MDS) codes is considered. This combines previous works on PIR schemes based on transitive non-MDS codes on one hand, and PIR from MDS-coded Byzantine and nonresponsive servers on the other hand. More specifically, a PIR scheme employing binary Reed-Muller (RM) codes tolerant to colluding, Byzantine, and non-responsive servers is constructed, and bounds for the achievable rates are derived under certain conditions. The construction of such schemes turns out to be much more involved than for MDS codes. Namely, the binary query vectors have to be selected with great care to hit the desired information sets, which is technically challenging as will be shown.