Secure Quantum Network Code without Classical Communication

We consider the secure quantum communication over a network with the presence of the malicious adversary who can eavesdrop and contaminate the states. The network consists of the noiseless quantum channels with unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m(1) of the attacked channels over the entire network uses is less than a half of network transmission rate m(0) (i.e., m(1) < m(0)/2), our protocol implements secret and correctable quantum communication of rate m(0)-2m(1) by using the network asymptotic number of times. Our protocol requires no classical communication and no knowledge of network structure, but instead, a node operation is limited to the application of an invertible matrix to the basis states. Our protocol can be thought of as a generalization of honest-dealer verifiable quantum secret sharing. A full version of this paper is accessible at: https://arxiv.org/pdf/1801.03306.pdf.