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

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-03-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
14
885-898
Series
IEEE Journal on Selected Areas in Communications, Volume 40, issue 3
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.
Description
Publisher Copyright: © 1983-2012 IEEE.
Keywords
capacity, information theoretic privacy, Private information retrieval (PIR), quantum information theory
Other note
Citation
Allaix, M, Song, S, Holzbaur, L, Pllaha, T, Hayashi, M & Hollanti, C 2022, ' On the Capacity of Quantum Private Information Retrieval From MDS-Coded and Colluding Servers ', IEEE Journal on Selected Areas in Communications, vol. 40, no. 3, pp. 885-898 . https://doi.org/10.1109/JSAC.2022.3142363