Quantum Private Information Retrieval with Sublinear Communication Complexity

This note presents a quantum protocol for private information retrieval, in the single-server case and with information-theoretical privacy, that has O(\sqrt{n})-qubit communication complexity, where n denotes the size of the database. In comparison, it is known that any classical protocol must use \Omega(n) bits of communication in this setting.

💡 Research Summary

The paper addresses the classic Private Information Retrieval (PIR) problem in the single‑server, information‑theoretic privacy setting, and shows that quantum communication can break the linear‑communication barrier that is unavoidable for classical protocols. In the classical model, any PIR protocol must transmit Ω(n) bits, where n is the size of the database (Chor et al., 1998). Earlier quantum work (Kerenidis & de Wolf, 2004) proved that any two‑message quantum PIR protocol also requires linear communication, suggesting that quantum mechanics does not help in this setting.

The authors present a three‑message quantum protocol that achieves O(√n) qubits of total communication. The database is modeled as A = (a₁,…,a_ℓ) where each a_k is an r‑bit string (so the total number of bits is ℓ·r = n). The user holds an index i ∈ {1,…,ℓ}. The protocol proceeds as follows:

1. State preparation (Server → User). The server creates the entangled state
   \