Tree-graph quantum broadcasting: resource state preparation and cascading gate teleportations

In the works [Phys. Rev. A 105, 042611 (2022), Phys. Rev. A 107, 062605 (2023)], we demonstrated how qubit states of a restricted form can be simultaneously transmitted to multiple receivers. In the original construction, one or more senders can apply phase gates—parameters that senders can use to encode information—after distributing an entangled state. This is followed by the sender's measurement and classical communication of the results to the receivers. We extend this quantum broadcasting problem to a multi-layer broadcasting setup, constructing a tree-graph entangled state and demonstrating cascaded gate teleportations enabled by sequential measurements and classical communications. We also discuss preparation procedures for the entangled resource state and long-range entanglement, giving a connection between quantum communication tasks and condensed matter physics.