Multicasting homogeneous and heterogeneous quantum states in quantum networks

In this paper, we target the practical implementation issues of quantum multicast networks. First, we design a recursive lossless compression that allows us to control the trade-off between the circuit complexity and the dimension of the compressed quantum state. A formula that describes the trade-off is given, and we further analyze how the formula is affected by the controlling parameter of the recursive procedure. Our recursive lossless compression can be applied in a quantum multicast network where the source outputs homogeneous quantum states (many copies of a quantum state), and intends to send the quantum state to each destination through a bottleneck. Such recursive lossless compression is extremely useful in the current situation where the technology of producing a large scale quantum circuit is limited. Second, we develop two lossless compression schemes that work for heterogenous quantum states (many copies of a set of quantum states) when the set of quantum states satisfies a certain structure. The heterogenous compression schemes provide extra compressing power over the homogenous compression scheme. Finally, we realize our heterogenous compression schemes in several quantum multicast networks, including the single-source multi-terminal model, the multi-source multi-terminal model, and the ring networks, and analyze the bandwidth requirements for these network models.