Quantum private information retrieval over a collective noisy channel

Quantum Private Information Retrieval (QPIR) allows a user (Alice) to retrieve a database item from the database owned by the database holder (Bob) in such a way that Alice can query only the database item she wants, but cannot get other items, and Bob does not know which item Alice queries. However, the real quantum channel between Alice and Bob is noisy, and the noise may result in not only the chance that Alice obtains a false item, but also that both parties may cheat by camouflaging themselves with noise. In this paper, we use the decoherence-free subspace (DFS) for QPIR, which we call DFS-QPIR. The DFS-QPIR protocol removes the effect of the channel noise on the errors in the retrieved item so that two parties cannot cheat by replacing the noisy channel with a noiseless one. It can work over a collective noisy channel while retaining high reliability, database security and user privacy simultaneously. While only the collective unitary noise is taken into account, the proposed DFS-QPIR protocol can be straightforwardly extended to more general collective noise channel.