Routing algebras for quantum network

The practical implementation of quantum communication relies on having efficient quantum networks and robust communication algorithms. In order to overcome the distance limitations imposed by entanglement decay, networks of quantum repeaters are required to extend the range of short-range entangled states through entanglement swapping and to increase the fidelity of the distributed entangled state through entannglement distillation. An important challenge is to find the paths through a complex quantum network that optimize the entanglement distribution rate between any two arbitrary nodes. We introduce an extension to the standard formulation of routing algebras, and we use this to develop an algorithm to find the optimal path when considering quantum networks which allow both entanglement swapping and entanglement distillation as their fundamental operations.