An information-theoretic model is presented for a general quantum physically unclonable function (QPUF) that generates a bipartite classical-quantum output. We first define achievable secret key rate versus privacy leakage rate pairs featuring perfect secrecy and uniform distribution of the secret key. To analyze the secret key generation from this QPUF model, we focus on two cases: first, without any constraints on the storage of public information, i.e., the helper data, and second, with rate constraints on it. This, in turn, provides a solution for the case of privacy leakage constraint. We calculate the maximum secret key that a QPUF can generate and derive the capacity region corresponding to this definition of achievability.