Impossibility of Quantum Private Queries

Abstract

Symmetric private information retrieval is a cryptographic task allowing a user to query a database and obtain exactly one entry without revealing to the owner of the database which element was accessed. The task is a variant of general two-party protocols called one-sided secure function evaluation and is closely related to oblivious transfer. Under the name quantum private queries, quantum protocols have been proposed to solve this problem in a cheat-sensitive way: In such protocols, it is not impossible for dishonest participants to cheat, but they risk detection [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 100, 230502 (2008)]. We give an explicit attack against any cheat-sensitive symmetric private information retrieval protocol, showing that any protocol that is secure for the user cannot have non-trivial security guarantees for the owner of the database.

v2,v3,v4: Minor changes. v5: Updated to the journal-published version; scientific content unchanged, with only minor editorial and stylistic changes. Building on the present proof techniques, arXiv:2405.12121 shows lower bounds for quantum secure function evaluation reductions