Quantum State Transmission Over Partially Corrupted Quantum Information Network

Quantum communication over network is particularly appealing in a similar way to classical network communication, but a partially corrupted quantum network has not been sufficiently studied. We discuss quantum state transmission over a partially corrupted quantum network, in which the sender transmits m(0) qudits, i.e., d-level systems, to the receiver via network, but m(1) channels are corrupted. As our result, we show that the optimal transmission rate is at least (m(0) - 2m(1) + 1) log d under the following two settings. In the first case, the unitaries on intermediate nodes are arbitrary and the corruptions on the m1 channels are individual. In the second case, the unitaries on intermediate nodes are restricted to Clifford operations and the corruptions on the m(1) channels are adaptive, i.e., they are caused by an attack with a quantum memory. Further, our code in the second case realizes the noiseless communication even with the single-shot setting and is constructed dependently only on the network topology and the places of the m(1) corrupted channels.