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Information-Theoretic Aspects of Quantum Private Information Retrieval

Seunghoan Song

Published Dec 28, 2020• 0 citations
OpenAlex

Abstract

When a user retrieves information from databases, it is often required to protect the privacy of the user.Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of 𝑓𝑓 messages from non-communicating 𝑛𝑛 servers by downloading quantum systems without revealing the identity of the retrieved message to any individual server.Symmetric QPIR is a QPIR with server secrecy in which the user obtains no information of non-targeted messages.This thesis investigates the fundamental communication limit of the symmetric and nonsymmetric QPIR and constructs the optimal QPIR protocols achieving the communication limit.The communication cost of a QPIR protocol is evaluated by the QPIR rate defined as

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Capacity of Quantum Private Information Retrieval with Colluding Servers

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Quantum private information retrieval (QPIR) is a protocol that a user retrieves one of f files from non-communicating n servers by downloading quantum systems without revealing the identity of the target file. As variants of the QPIR with stronger security requirements, the symmetric QPIR is that the files except for the target file are not leaked to the user, and the t-private QPIR is that the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the one file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min {1, 2(n - t)/n} for any 1 ≤ t <; n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2020•7 citations

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Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct two-server symmetric QPIR protocols for pure states. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.

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Capacity of Quantum Symmetric Private Information Retrieval With Collusion of All But One of Servers

Seunghoan Song, Masahito Hayashi

Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple classical files by downloading quantum systems from non-communicating n servers each of which contains a copy of all files, while the identity of the retrieved file is unknown to each server. Symmetric QPIR (QSPIR) is QPIR in which the user only obtains the queried file but no other information of the other files. In this article, we consider the (n-1)-private QSPIR in which the identity of the retrieved file is secret even if any n-1 servers collude, and derive the QSPIR capacity for this problem which is defined as the maximum ratio of the retrieved file size to the total size of the downloaded quantum systems. For any even number n of servers, we show that the capacity of the (n-1)-private QSPIR is 2/n, when we assume that there are prior entanglements among the servers. We construct an (n-1)-private QSPIR protocol of rate ⌈n/2⌉-1and prove that the capacity is upper bounded by 2/n even if any error probability is allowed. The (n-1)-private QSPIR capacity is strictly greater than the classical counterpart.

arXiv:1903.12556•IEEE Journal on Selected Areas in Information Theory•Jan 26, 2021•19 citations
When a user retrieves information from databases, it is often required to protect the privacy of the user.Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of 𝑓𝑓 messages from non-communicating 𝑛𝑛 servers by downloading quantum systems without revealing the identity of the retrieved message to any individual server.Symmetric QPIR is a QPIR with server secrecy in which the user obtains no information of non-targeted messages.This thesis investigates the fundamental communication limit of the symmetric and nonsymmetric QPIR and constructs the optimal QPIR protocols achieving the communication limit.The communication cost of a QPIR protocol is evaluated by the QPIR rate defined as
Quantum private information retrieval (QPIR) is a protocol that a user retrieves one of f files from non-communicating n servers by downloading quantum systems without revealing the identity of the target file. As variants of the QPIR with stronger security requirements, the symmetric QPIR is that the files except for the target file are not leaked to the user, and the t-private QPIR is that the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the one file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min {1, 2(n - t)/n} for any 1 ≤ t <; n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.
Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct two-server symmetric QPIR protocols for pure states. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.
Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple files from n\mathsf{n}n non-communicating servers by downloading quantum systems without revealing which file is retrieved. As variants of QPIR with stronger security requirements, symmetric QPIR is a protocol in which no other files than the target file are leaked to the user, and t\mathsf{t}t-private QPIR is a protocol in which the identity of the target file is kept secret even if at most t\mathsf{t}t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the file size to the size of downloaded quantum systems, and we prove that the symmetric t\mathsf{t}t-private QPIR capacity is min⁡{1,2(n−t)/n}\min\{1,2(\mathsf{n}-\mathsf{t})/\mathsf{n}\}min{1,2(n−t)/n} for any 1≤t<n1\leq \mathsf{t}< \mathsf{n}1≤t<n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.
Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple files from n non-communicating servers by downloading quantum systems without revealing which file is retrieved. As variants of QPIR with stronger security requirements, symmetric QPIR is a protocol in which no other files than the target file are leaked to the user, and t-private QPIR is a protocol in which the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min{1,2( n- t)/ n} for any 1 ≤ t <; n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.
In the era of extensive data growth, robust and efficient mechanisms are needed to store and manage vast amounts of digital information, such as Data Storage Systems (DSSs). Concurrently, privacy concerns have arisen, leading to the development of techniques like Private Information Retrieval (PIR) to enable data access while preserving privacy. A PIR protocol allows users to retrieve information from a database without revealing the specifics of their query or the data they are accessing. With the advent of quantum computing, researchers have explored the potential of using quantum systems to enhance privacy in information retrieval. In a Quantum Private Information Retrieval (QPIR) protocol, a user can retrieve information from a database by downloading quantum systems from multiple servers, while ensuring that the servers remain oblivious to the specific information being accessed. This scenario offers a unique advantage by leveraging the inherent properties of quantum systems to provide enhanced privacy guarantees and improved communication rates compared to classical PIR protocols. In this thesis we consider the QPIR setting where the queries and the coded storage systems are classical, while the responses from the servers are quantum. This problem was treated by Song et al. for replicated storage and different collusion patterns. This thesis aims to develop QPIR protocols for coded storage by combining known classical PIR protocols with quantum communication algorithms, achieving enhanced privacy and communication costs. We consider different storage codes and robustness assumptions, and we prove that the achieved communication cost is always lower than the classical counterparts.
Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple classical files by downloading quantum systems from non-communicating n servers each of which contains a copy of all files, while the identity of the retrieved file is unknown to each server. Symmetric QPIR (QSPIR) is QPIR in which the user only obtains the queried file but no other information of the other files. In this article, we consider the (n-1)-private QSPIR in which the identity of the retrieved file is secret even if any n-1 servers collude, and derive the QSPIR capacity for this problem which is defined as the maximum ratio of the retrieved file size to the total size of the downloaded quantum systems. For any even number n of servers, we show that the capacity of the (n-1)-private QSPIR is 2/n, when we assume that there are prior entanglements among the servers. We construct an (n-1)-private QSPIR protocol of rate ⌈n/2⌉-1and prove that the capacity is upper bounded by 2/n even if any error probability is allowed. The (n-1)-private QSPIR capacity is strictly greater than the classical counterpart.