We consider quantum multicast networks in which quantum states generated by multiple sources have to be simultaneously delivered to multiple receivers. We demonstrate that in addition to the apparent similarity to the multicommodity flow problems, quantum networks, to a certain extent, behave as classical communication networks. In particular, we show that lossless compression of special multicast quantum states is possible and significantly reduces the edge capacity requirements of the multicast.
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
qr-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.
Multicast of unknown quantum states is an unavoidable issue in the construction of quantum networks. Most existing quantum network coding schemes can only restore an unknown state at one of the target nodes during multicast. In this paper, we propose a quantum network coding scheme to multicast unknown quantum states in networks with linear network coding. Concretely, GHZ states are generated between each sender and all receivers. Unknown states are then sent and stored in the entangled state shared by the receivers. Finally, the receivers use asymmetric optimal universal cloning to obtain the required states. The scheme achieved to multicast within 1 quantum transmission and 2 classical transmissions in networks with constrained classical communication. Compared to other schemes, our scheme allows receivers to autonomously adjust the fidelity without the sender knowing the requirements.