How Bob in Quantum Private Query Protocol Gets the Element?

Quantum private query (QPQ) requires that the database holder Bob knows nothing about his client Alice, including the index she provides and the element she obtains. However, on some occasion, Bob wants to know which element he has revealed to Alice. Therefore, we raise a symmetric quantum private query (SQPQ) problem in this paper. SQPQ can guarantee that Alice shares the real element with Bob and also partially protect the privacy of Alice's index. Some necessary conditions are need to satisfy to implement SQPQ. We prove that Alice must provide some extra information to enable Bob to know the element. Then, we define the term “absolutely secure”, which is a security notion stronger than cheat sensitive, and prove that “absolutely secure”SQPQ is impossible. In addition, we raise a cheat sensitive scheme three-databases-detection to implement SQPQ protocol. Finally, we construct a reduction from SQPQ to quantum bit commitment (QBC) to clarify that SQPQ is a problem more difficult than QBC.