Range query in cloud-based outsourcing applications is an important data search service, but it can suffer from privacy disclosure. In this paper, to enhance the security and privacy of sensitive data, we introduce quantum cryptographic technologies and present a feasible quantum approach to address an important range query, i.e., privacy-preserving range MAX/MIN query. First, we define a primitive protocol of secure multiparty computations, called Oblivious Set Inclusion Decision (OSID), in which two parties jointly decide whether a private set includes another private set in an oblivious way, and present an efficient OSID quantum protocol. Especially, in order to efficiently implement OSID quantum protocol, we design a single-photon-based quantum protocol for computing XOR of two private bits, which can achieve the information-theoretical security with the help of a non-colluding quantum cloud. Finally, we propose a novel quantum scheme for privacy-preserving range MAX/MIN query in edge-based Internet of Things by using OSID quantum protocols. Compared with the classical related schemes, our proposed quantum scheme has higher security (i.e., quantum security), because the security of our proposed protocols is based on the basic physical principles of quantum mechanics, instead of unproven computational difficulty assumptions.