  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. We give a formula that describes the
trade-off, and 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) to a set of destinations
through a bottleneck. Such a recursive lossless compression is extremely useful
in the current situation where the technology of producing large-scale quantum
circuits is limited. Second, we develop two lossless compression schemes that
work for heterogeneous quantum states (many copies of a set of quantum states)
when the set of quantum states satisfies a certain structure. The heterogeneous
compression schemes provide extra compressing power over the homogeneous
compression scheme. Finally, we realize our heterogeneous compression schemes
in several quantum multicast networks, including the single-source
multi-terminal model, the multi-source multi-terminal model, and the ring
networks. We then analyze the bandwidth requirements for these network models.
