Post-processing of the oblivious key in quantum private queries

Abstract: Quantum private query (QPQ) is a kind of quantum protocols to protect both users' privacy in their communication. There is an interesting example, that is, Alice wants to buy one item from Bob's database, which is composed of a quantity of valuable messages. QPQ protocol is the communication procedure ensuring that Alice can get only one item from Bob, and at the same time, Bob cannot know which one was taken by Alice. Owing to its practicability, quantum-key-distribution-based QPQ has draw much attention in recent years. However, the post-processing of the key in such protocols, called oblivious key, remains far from being satisfactorily known. Especially, the error correction method for such special key is still missing. Here we focus on the post-processing of the oblivious key, including both dilution and error correction. On the one hand, we demonstrate that the previous dilution method, which greatly reduces the communication complexity, will bring Alice the chance to illegally obtain much additional information about Bob's database. Simulations show that by very limited queries Alice can obtain the whole database. On the other hand, we present an effective error-correction method for the oblivious key, which completes its post-processing and makes such QPQ more practical.