The phenomenal progress in quantum technologies over the past decades has laid the groundwork for the construction of quantum networks, which will channel the power of quantum theory to guarantee secure and efficient communication, computation, and much more. This thesis studies the notion of trust in quantum networks. In our information age, protecting the security or anonymity of data is a key requirement. We investigate certain protocols that are fundamental to the operation and applications of quantum networks, and propose ways to test and analyse their security, in spite of adversarial intervention. Our focus is on practical methods of verifying the untrusted components, which could be incorporated into realistic networks in the near future.
To begin, we propose a protocol for authenticated communication of quantum messages, by verifying the entanglement required for quantum teleportation in an experimentally feasible way. We model the performance of our scheme in the presence of noise. Furthermore, we explore such an authenticated teleportation in the one-sided device-independent scenario, where some devices used for verification may be corrupted. We derive error-tolerant self- testing bounds and extend our results to a realistic experimental setting, demonstrating the compatibility of our protocol with state-of-the-art technology. We then study anonymity, an essential feature for communication across networks. Combining the power of classical and quantum subroutines, we build a practical protocol for anonymous communication of quantum messages, without the need to trust the players in our network, their computational power, or the entanglement they share. We end by considering the verification of graph states distributed across a network of possibly dishonest players, applying our scheme to specific graph states that are central to quantum communication and computation schemes.