Capacities of Entanglement Distribution From a Central Source

Abstract: Distribution of entanglement is an essential task in quantum information processing and the realization of quantum networks. In our work, we theoretically investigate the scenario where a central source prepares an N-partite entangled state and transmits each entangled subsystem to one of N receivers through noisy quantum channels. The receivers are then able to perform local operations assisted by unlimited classical communication to distill target entangled states from the noisy channel output. In this operational context, we define the EPR distribution capacity and the GHZ distribution capacity of a quantum channel as the largest rates at which Einstein-Podolsky-Rosen (EPR) states and Greenberger-Horne-Zeilinger (GHZ) states can be faithfully distributed through the channel, respectively. We establish lower and upper bounds on the EPR distribution capacity by connecting it with the task of assisted entanglement distillation. We also construct an explicit protocol consisting of a combination of a quantum communication code and a classical-post-processing-assisted entanglement generation code, which yields a simple achievable lower bound for generic channels. As applications of these results, we give an exact expression for the EPR distribution capacity over two erasure channels and bounds on the EPR distribution capacity over two generalized amplitude damping channels. We also bound the GHZ distribution capacity, which results in an exact characterization of the GHZ distribution capacity when the most noisy channel is a dephasing channel.