In this paper, we show that the principle of quantum cryptography can be applied not only to a key distribution scheme but also to a data transmission scheme. We propose a secure data transmission scheme in which an eavesdropping can be detected based on sharing the bases Alice (the sender) and Bob (the receiver) have. We also show properties of this scheme.

In quantum communication theory, a realization of the optimum quantum receiver that minimizes the error probability is one of fundamental problems. A quantum receiver is described by detection operators. Therefore, it is very important to derive the optimum detection operators for a realization of the optimum quantum receiver. In general, it is difficult to derive the optimum detection operators, except for some simple cases. In addition, even if we could derive the optimum detection operators, it is not trivial what device corresponds to the operators. In this paper, we show a realization method of a quantum receiver which is described by a projection-valued measure (PVM) and apply the method to 3-ary phase-shift-keyed (3PSK) coherent-state signals.

Recently, the quantum information theory attracts much attention. In quantum information theory, the existence of superadditivity in capacity of a quantum channel was foreseen conventionally. So far, some examples of codes which show the superadditivity in capacity have been clarified. However in present stage, characteristics of superadditivity are not still clear up enough. The reason is as follows. All examples were shown by calculating the mutual information by quantum combined measurement, so that one had to solve the eigenvalue and the eigenvector problems. In this paper, we construct a simplification algorithm to calculate the mutual information by using square-root measurement as decoding process of quantum combined measurement. The eigenvalue and the eigenvector problems are avoided in the algorithm by using group covariancy of binary linear codes. Moreover, we derive the analytical solution of the mutual information for parity check codes with any length as an example of applying the simplification algorithm.