Multicast quantum network coding as optimal symmetric universal cloning over a quantum network

Abstract

We study the problem of perfectly multicasting symmetric universal clones of unknown quantum states over quantum networks with free classical communication. We construct a protocol that multicasts symmetric universal clones of input states from multiple source nodes by extending the quantum network coding protocol proposed by Kobayashi et al. We further establish a sufficient condition for perfect multicast in the single-source setting. Specifically, we show that when a single copy of a $q^r$-dimensional input state is available at the source node, where $q$ is a sufficiently large prime power, perfect multicast of the corresponding symmetric universal clone is achievable using a small amount of entanglement shared among the target nodes. This result holds for quantum networks represented by an undirected graph $G$, where each edge corresponds to a noiseless $q$-dimensional quantum channel, provided that there exists an acyclic directed graph $G^{\prime }$ obtained by assigning directions to the edges of $G$ such that the minimum cut of $G^{\prime }$ is at least $r$.

25 pages, 1 figures. Published in Lecture Notes in Electrical Engineering (LNEE), vol. 1634. Presented at the 6th International Conference on Nano Electronics Research and Education (ICNERE2025) Joint with the 27th Takayanagi Kenjiro Memorial Symposium