Capacity of Quantum Private Information Retrieval With Multiple Servers

Abstract

We study the capacity of quantum private information retrieval (QPIR) with multiple servers. In the QPIR problem with multiple servers, a user retrieves a classical file by downloading quantum systems from multiple servers each of which contains the copy of a classical file set while the identity of the downloaded file is not leaked to each server. The QPIR capacity is defined as the maximum rate of the file size over the whole dimension of the downloaded quantum systems. When the servers are assumed to share prior entanglement, we prove that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files. We construct a rate-one protocol only with two servers. This capacity-achieving protocol outperforms its classical counterpart in the sense of the capacity, server secrecy, and upload cost. The strong converse bound is derived concisely without using any secrecy condition. We also prove that the capacity of multi-round QPIR is 1.

Provably Secure Symmetric Private Information Retrieval with Quantum Cryptography

“…The relaxation made to the SPIR definition would allow us to use another protocol used as the foundation for Song et al's quantum SPIR protocol [26]. In this protocol, we label the user's desired bit as w i (n) = n…”

“…Kerenidis et al focuses on how SPIR can be performed without shared randomness if the user is honest [25]. Song et al proposed a quantum multi-database SPIR, but requires shared entanglement between the data centres and assumes secure classical and quantum channels [26].…”

Capacity of Quantum Private Information Retrieval With Colluding Servers

“…When two-way quantum communication is allowed, Le Gall [23] proposed a one-server QPIR protocol whose communication complexity is the square root of the size of all files. Song and Hayashi [27], [28] discussed the QPIR capacity, which is the maximum ratio of the file size to the size of the downloaded quantum systems when the upload from the user to the servers is classical, the download is quantum, and the servers share entanglement before the protocol starts. They showed that the QPIR capacity is 1 and proposed a capacity-achieving QPIR protocol with only two servers.…”

“…In the quantum case, the paper [21] proved that symmetric QPIR can be implemented if two-way quantum communication is available. The paper [27] showed that symmetric QPIR is also possible with the classical upload, quantum download, and shared entanglement, and derived that the symmetric QPIR capacity is 1.…”

“…As a generalization of the QPIR capacities in [27], [28], we derive the symmetric t-private QPIR capacity for any t less than the number of servers n. Similar to the papers [27] and [28], we define the QPIR model as follows: a user retrieves one of f files from n non-communicating servers, each of which contains the whole classical file set; the servers share an entangled state before the protocol starts; the user uploads classical queries and downloads quantum systems; and the user decodes the target file by quantum measurement. The capacity is defined with four security parameters: error probability, server secrecy, user t-secrecy, and upload cost.…”