Secure Quantum Network Code without Classical Communication

We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m1 of the attacked channels over the entire network uses is less than a half of the network transmission rate m0 (i.e., m1 < m0 / 2), our code implements secret and correctable quantum communication of the rate m0 - 2m1 by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing.