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arXiv · 2608.18471

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

Go Kato·Mio Murao·Masaki Owari
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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 $G'$ obtained by assigning directions to the edges of $G$ such that the minimum cut of $G'$ is at least $r$.

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Go Kato, Mio Murao, Masaki Owari. 2026-08-19. Multicast quantum network coding as optimal symmetric universal cloning over a quantum network. https://doi.org/10.1007/978-3-032-25259-3_26

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