An input-randomness-free device-independent cryptographic protocol for quantum networks

As our foundational understanding of quantum information theory broadens, it remains to be seen whether novel foundational developments will lead to corresponding applications. Promising branches are quantum networks and quantum cryptography, which are more intertwined by the day. In particular, a fascinating phenomena is that in networks with independent sources, Bell nonlocality can take place without the need for measurement settings for the parties, i.e. in each round, each source is asked to produce the same state and each party measures the same measurement. This is in stark contrast to standard Bell nonlocality, where seed randomness is necessary to certify nonlocality and through it, randomness of the outcomes. Building on nonlocality without seed randomness in networks, we propose a device-independent quantum key distribution protocol (which can be extended to quantum conference key agreement if it involves more than 2 parties) which allows for the generation of shared secret keys without the need for input randomness. We rely on recent results on nonlocality in networks and its robustness, showing how in a ring network with $N$ bipartite sources, one must only make standard assumptions in order to run the protocol, while no trust is required from the devices themselves. We thus give a device-independent proof of security under this network assumption in the IID setting. In summary, we propose a first-of-a-kind protocol for Device-Independent Quantum Key Distribution which is native to the network setting, and which does not demand input randomness from the parties in order to produce output randomness.