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International journal of applied research

A survey on communication complexity in quantum private information retrieval: Efficiency challenges and advances

Laxmi Kumari, Tarun Kumar Mahato

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.22271/allresearch.2025.v11.i6a.12630

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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.
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) 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 propose a quantum solution to the classical private information retrieval (PIR) problem, which allows one to query a database in a private manner. The protocol offers privacy thresholds and allows the user to obtain information from a database in a way that offers the potential adversary, in this model the database owner, no possibility of deterministically establishing the query contents. This protocol may also be viewed as a solution to the symmetrically private information retrieval problem in that it can offer database security (inability for a querying user to steal its contents). Compared to classical solutions, the protocol offers substantial improvement in terms of communication complexity. In comparison with the recent quantum private queries [Phys. Rev. Lett. 100, 230502 (2008)] protocol, it is more efficient in terms of communication complexity and the number of rounds, while offering a clear privacy parameter. We discuss the security of the protocol and analyze its strengths and conclude that using this technique makes it challenging to obtain the unconditional (in the information-theoretic sense) privacy degree; nevertheless, in addition to being simple, the protocol still offers a privacy level. The oracle used in the protocol is inspired both by the classical computational PIR solutions as well as the Deutsch-Jozsa oracle.
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.