In 2009, Broadbent, Fitzsimons and Kashefi proposed a quantum secure delegated computation scheme (a.k.a. Blind Quantum Computation). Since then, many researches on quantum cloud computing have intensively investigated. In this talk, we extend the BKF protocol so that the server Bob can own his input and introduce a notion of “partial” BQC. Some cryptographic protocols can be discussed in the new framework. We take Private Information Retrieval and provide a quantum PIR protocol based on the partial BQC. Our QPIR protocol is advantageous in the sense that its communication complexity is of polylog N, where N is the database size. Also, we discuss relations to lower bounds of quantum communication complexity of QPIR.