Security in Quantum Networks as an Optimization Problem

We present a general framework for casting the problem of designing secure quantum networks into a classical optimization problem. We introduce a measure of risk that serves as upper bound on the probability of loosing a message to the adversary. Based on this results, we can transform the problem of secure network design into an optimization procedure, which opens the field for the entire framework of optimization theory to tackle the problem most efficiently. The latter is particularly appealing, since we prove the problem to be NP-hard in general. Our methodology is formulated to yield results that have interpretations in probabilistic terms, but can be generalized to other settings in a straightforward manner. The modeling approach is simple, and naturally accounts for different notions of security, depending on the situation at hand. Furthermore, our results are not limited to security in quantum networks, as we rely on quantum cryptography only to the extent of securing links. Hence, the analysis is equally applicable for any (multipath) transmission setup, where information-theoretic security is demanded.