Physical Unclonable Functions (PUFs) are physical devices with unique behavior that are hard to clone. A variety of PUF schemes have been considered in theoretical studies as well as practical implementations of several security primitives such as identification and key generation. Recently, the inherent unclonability of quantum states has been exploited for defining (a partial) quantum analogue to classical PUFs (against limited adversaries). There are also a few proposals for quantum implementations of classical optical PUFs. However, none of these attempts provides a comprehensive study of Quantum Physical Unclonable Functions (QPUFs) with quantum cryptographic tools as we present in this paper. We formally define QPUFs, encapsulating all requirements of classical PUFs as well as introducing new ones inherent to the quantum setting such as testability. We develop a quantum game-based security framework for our analysis and define a new class of quantum attacks, called General Quantum Emulation Attack. This class of attacks exploits previously captured valid challenge-response pairs to emulate the action of an unknown quantum transformation on new input. We devise a concrete attack based on an existing quantum emulation algorithm and use it to show that a family of quantum cryptographic primitives that rely on unknown unitary transformations do not provide existential unforgeability while they provide selective unforgeability. Then, we express our results in the case of QPUF as an unknown unitary transformation.