Quantum repeaters based on CNOT gate under decoherence

In this paper, we study single-qubit and single-user quantum repeaters based on CNOT gates under decoherence using the Kraus-operator representations of decoherence. We investigate the influence of decoherence on the information-disturbance trade-off of quantum repeaters. It is found that decoherence may lead to the appearance of three subspaces, called as the normal subspace, the anomalous subspace, and the decoherence-free subspace (DFS), respectively. It is indicated that in the normal subspace decoherence decreases the transmission and estimation fidelities, in the anomalous subspace decoherence enhances these fidelities, and in the DFS these fidelities do not change. The concept of the quality factor is introduced to evaluate the quality of the quantum repeater. It is indicated that the quality factor can be efficiently controlled and manipulated by changing the initial state of the probe qubit. It is found that under certain conditions the quantum repeater can be optimal even in the presence of decoherence.