Asymmetric Quantum Multicast Network Coding: Asymmetric Optimal Cloning over Quantum Networks

Multicasting of quantum states is an essential feature of quantum internet. Since the noncloning theorem prohibits perfect cloning of an unknown quantum state, an appropriate protocol may depend on the purpose of the multicast. In this paper, we treat the multicasting of a single copy of an unknown state over a quantum network with free classical communication. We especially focus on protocols exactly multicasting an asymmetric optimal universal clone. Hence, these protocols are optimal and universal in terms of mean fidelity between input and output states, but the fidelities can depend on target nodes. Among these protocols, a protocol spending smaller communication resources is preferable. Here, we construct such a protocol attaining the min-cut of the network described as follows. Two (three) asymmetric optimal clones of an input state are created at a source node. Then, the state is divided into classical information and a compressed quantum state. The state is sent to two (three) target nodes using the quantum network coding. Finally, the asymmetric clones are reconstructed using LOCC with a small amount of entanglement shared among the target nodes and the classical information sent from the source node.