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arXiv:2304.05125 · EPJ Quantum Technology

Prior entanglement exponentially improves one-server quantum private information retrieval for quantum messages

Seunghoan Song, François Le Gall, Masahito Hayashi

Published Sep 6, 2024• 2 citations
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Abstract

Quantum private information retrieval (QPIR) for quantum messages is a quantum communication task, in which a user retrieves one of the multiple quantum states from the server without revealing which state is retrieved. In the one-server setting, we find an exponential gap in the communication complexities between the presence and absence of prior entanglement in this problem with the one-server setting. To achieve this aim, as the first step, we prove that the trivial solution of downloading all messages is optimal under QPIR for quantum messages, which is a similar result to that of classical PIR but different from QPIR for classical messages. As the second step, we propose an efficient one-server one-round QPIR protocol with prior entanglement by constructing a reduction from a QPIR protocol for classical messages to a QPIR protocol for quantum messages in the presence of prior entanglement.

DOI
10.1140/epjqt/s40507-024-00266-6

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Quantum private information retrieval (QPIR) for quantum messages is a quantum communication task, in which a user retrieves one of the multiple quantum states from the server without revealing which state is retrieved. In the one-server setting, we find an exponential gap in the communication complexities between the presence and absence of prior entanglement in this problem with the one-server setting. To achieve this aim, as the first step, we prove that the trivial solution of downloading all messages is optimal under QPIR for quantum messages, which is a similar result to that of classical PIR but different from QPIR for classical messages. As the second step, we propose an efficient one-server one-round QPIR protocol with prior entanglement by constructing a reduction from a QPIR protocol for classical messages to a QPIR protocol for quantum messages in the presence of prior entanglement.
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.
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.
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
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 containing the whole classical file set, without revealing the identity of the retrieved file to any individual server. The QPIR capacity is defined as the maximum rate of the file size over the whole dimension of the downloaded quantum systems. Assuming the preexisting entanglement among servers, we prove that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files. We propose a rate-one protocol which can be implemented by using only 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 the secrecy conditions.
Quantum Private Information Retrieval (QPIR) is a new and growing area that uses quantum computing to improve privacy and efficiency in database searches. Traditional Private Information Retrieval (PIR) methods often require a large amount of communication between the user and the server, making them slow and costly. QPIR aims to solve this problem by using quantum techniques like superposition and entanglement to reduce communication while keeping the user’s query private. In this paper, we review different QPIR methods and analyze how they handle communication complexity. We compare multi-server and single-server models, discussing their strengths and weaknesses. We also explore the practical challenges of QPIR, such as the need for quantum resources, errors in quantum systems, and security against quantum attackers. Additionally, we highlight important research gaps, including how to make single-server QPIR more efficient, balancing security with speed, and understanding how future quantum computers might impact QPIR security. By addressing these challenges, this survey aims to support further research and help develop practical, efficient, and secure QPIR systems for real-world use.
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.