On the Capacity of Quantum Private Information Retrieval from MDS-Coded and Colluding Servers

TL;DR

This paper investigates the maximum efficiency of quantum private information retrieval from MDS-coded and colluding servers, introducing new classes of QPIR and deriving their capacities, with implications for quantum and classical PIR schemes.

Contribution

It defines stabilizer and dimension-squared QPIR, derives their capacities, and establishes bounds relating quantum and classical PIR capacities, advancing understanding of quantum PIR limits.

Findings

Derived QPIR capacities for non-colluding servers as file number approaches infinity.

Established upper bounds on QPIR capacities based on classical PIR capacities.

Proposed a capacity-achieving scheme combining star-product and stabilizer QPIR methods.

Abstract

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.