Quantum excitation transfer in bosonic networks: a bipartite-graph framework

Highly efficient transfer of quantum resources including quantum excitations, states, and information on quantum networks is an important task in quantum information science. Here, we propose a bipartite-graph framework for studying quantum excitation transfer in bosonic networks by diagonalizing the intermediate sub-network between the sender and the receiver to construct a bipartite-graph configuration. We examine the statistical properties of the bosonic networks in both the original and bipartite-graph representations. In particular, we investigate quantum excitation transfer in both the finite and infinite intermediate-normal-mode cases, and show the dependence of the transfer efficiency on the network configurations and system parameters. We find the bound of maximally transferred excitations for various network configurations and reveal the underlying physical mechanisms. We also find that the dark-mode effect will degrade the excitation transfer efficiency. Our findings provide a new insight for the design and optimization of quantum networks.