Improvements about processing of measurement results in quantum repeater

In quantum repeater protocols, measurements are performed in multiple relay points. Classical communications are used to convey the measurement results. It is important to improve the way of conveying the measurement results so that EPR pairs are not affected by noises during classical communications. One solution is execution in the blind mode. In the blind mode, correction operations of multiple ES operations and multiple EPP operations are performed in a lump after EPR pairs are shared between the sender and the receiver. That is, the following quantum operations are performed without performing correction operations of the former quantum operations. The protocol in the conventional blind mode uses concatenated CSS codes. Therefore, the number of qubits gets large as the communication distance gets long. This paper proposes quantum repeater protocols which can be executed in the blind mode and can be constructed by using CSS codes of single encoding. This result shows that posterior processing can reduce the size of encoded states in some cases. Additionally, the results of this paper show that posterior processing can improve performance of error corrections in some cases. The proposed protocol with single encoding can correct large errors by setting some assumptions. In contrast, blind mode with single encoding can deal with small errors if propositions in this paper are not used. The key ideas in posterior processing are decomposition of errors and computations for comparing EPR pairs of different length.