There is a gap between properties of quantum and classical reliability functions. That is, the upper bound of the quantum reliability function diverges, whereas that of classical one does not, even if the same coherent signal is used. We are interested in the origin of this gap. In this paper, we investigate the upper bound of the reliability function for quantum signals coded by simplex codes when using square-root measurement (SRM). The reliability function in this case has a much steeper slope with respect to the rate than in the uncoded case. This result suggests the divergence of the upper bound of the quantum reliability function in the previous study.

Recently, the exact solution of the capacity of an attenuated quantum channel which is a model of a long distance optical fiber channel was derived [V. Giovannetti, et al., Phys. Rev. Lett. 90, 027902, (2004)]. In particular, the capacity of a broadband quantum channel, which is the ultimate limit of quantum communications, was shown. In this paper, we consider wavelength division multiplexing in order to attain the capacity of a broadband quantum channel.

A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are referred to as gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. The proposed algorithms exhibit better decoding performance than known BF algorithms, such as the weighted BF algorithm or the modified weighted BF algorithm for several LDPC codes.