Nowadays, network coding has been a very successful topic in information theory including many applications such as wireless networks while one of the simplest benefits is the efficient transmission in networks by allowing us to encode the transmitted information at every intermediate node. Since quantum information is much more expensive for communication than classical information, it was natural that this benefit made quantum researchers motivate the study of “quantum network coding.” This paper reports the current status of quantum network coding. At present, quantum network coding mostly means sending quantum information (rather than classical information) in a quantum network. Since quantum information cannot be cloned (the quantum no-cloning theorem), multiple unicast networks have been well-studied (in several settings). We present some of the known possibilities and limitations, and future works of quantum network coding, focusing on multiple unicast networks.
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