Multi-objective shortest paths for quantum networks

Finding optimal paths for entanglement distribution in a quantum network is a multi-objective shortest path (MOSP) problem. In order to use efficient MOSP algorithms, the network algebra must be both monotonic and isotonic, something that is not trivially true for general quantum networks. In this paper, we utilize the pairwise entangled network (PEN) state framework to present fusion rules for combining entangled resources along network edges and show that these fusion rules satisfy the necessary conditions of monotonicity and isotonicity. Using this, we present an algorithm for finding Pareto-optimal paths between source-destination pairs of vertices. We use this algorithm to analyze a variety of different networks, specifically focusing on the similarity of the Pareto-optimal paths between the two nodes.