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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> and the stabilizer QPIR scheme by Song <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> by employing (weakly) self-dual Reed–Solomon codes.
Highlights
With the amount of data stored in distributed storage systems steadily increasing, the demand for user privacy has surged in recent years
For stabilizer Quantum private information retrieval (PIR) (QPIR) and dimension-squared QPIR induced from strongly-linear PIR, we prove that the asymptotic QPIR/quantum symmetric PIR (QSPIR) capacities with maximum distance separable (MDS)-coded and colluding servers are min{1, 2(n − k − t + 1)/n}
The first result is the asymptotic capacity of stabilizer QPIR and dimension-squared QPIR induced from strongly linear PIR
Summary
With 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 user’s goal is to access a file of a (distributed) storage system without revealing the identity (index) of this desired file. In their seminal work Chor et al [2] introduced the concept of PIR from multiple non-colluding servers, each storing a copy of every file. This class is given by PIR schemes where both the computation of the server responses and the decoding of the desired file from these responses is achieved by applying linear functions.
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