On Quantum Advantage in Information Theoretic Single-Server PIR

In (single-server) Private Information Retrieval (PIR), a server holds a large database \({\mathtt {DB}}\) of size n, and a client holds an index \(i \in [n]\) and wishes to retrieve \({\mathtt {DB}}[i]\) without revealing i to the server. It is well known that information theoretic privacy even against an “honest but curious” server requires \(\varOmega (n)\) communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (“input purification attack”).

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