# Quantum Private Information Retrieval has Linear Communication Complexity

@article{Baumeler2014QuantumPI, title={Quantum Private Information Retrieval has Linear Communication Complexity}, author={{\"A}min Baumeler and Anne Broadbent}, journal={Journal of Cryptology}, year={2014}, volume={28}, pages={161-175} }

In private information retrieval (PIR), a client queries an $$n$$n-bit database in order to retrieve an entry of her choice, while maintaining privacy of her query value. Chor et al. [J ACM 45(6):965–981, 1998] showed that, in the information-theoretical setting, a linear amount of communication is required for classical PIR protocols (thus the trivial protocol is optimal). This linear lower bound was shown by Nayak [FOCS 1999, pp. 369–376, 1999] to hold also in the quantum setting. Here, we…

## 30 Citations

Security improvements of several basic quantum private query protocols with O(log N) communication complexity

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It is argued that the right notion of privacy of a communication protocol is the one assuming classical input registers, since otherwise the players can deviate considerably from the protocol.

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The goal is to minimise the amount of communication which takes place between the user and the database and allowing quantum bits as communication yields better Private Information Retrieval Schemes.

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The (n-1)-private QPIR capacity is strictly greater than the classical counterpart and it is proved that the capacity is upper bounded by $2/n$.

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The security of phase-encoded quantum private query (QPQ) is found to be vulnerable to a probabilistic entangle-and-measure attack performed by the owner of the database, and how to overcome this security loophole is discussed.

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In (single-server) Private Information Retrieval (PIR), a server holds a large database of size n, and a client holds an index \(i \in [n]\) and wishes to retrieve i without revealing i to the server.

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In the visible setting, it is proved that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages, and three two-server symmetric PIR protocols for pure states are constructed.

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The paper proved that the symmetric and non-symmetric QPIR capacities are 1.

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This work studies two different notions of quantum information cost and analyzes their relation, and provides new quantum protocols for the Inner Product function and for Private Information Retrieval, and shows that protocols for private information retrieval can have exponentially different information cost for the server.

Quantum Homomorphic Encryption for Polynomial-Sized Circuits

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A new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits, and a three-round scheme for blind delegated quantum computation which puts only very limited demands on the quantum abilities of the client.

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