For efficient use of energy in quantum communication, it is best to use discrete signals that approach the classical capacity achieved by a continuous input of coherent states. Analytical treatment of the classical communication channel requires discretization, and among such discrete signals, using signals as close as possible to the quantum channel capacity is ideal. The class of binary phase shift keying (BPSK) coherent-state signals has been proven to be optimal in the case of binary discretization; however, for multiary discretization with three or more signals, the optimal signals are unknown. In this study, we consider the case of ternary discretization. We numerically show that 3PSK is the optimal signal constellation in two dimensions.

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.

In recent years, significant progress has been made in the research on errors in quantum deletion/insertion channels along with the development of error-correcting codes. However, the current channel model may not be applicable in specific scenarios, such as when using coherent-state qubits as funda-mental qubits. Here, we materialize the conventional error model of synchronization errors to accommodate coherent-state qubits and their superposition states. Additionally, we quantitatively assess the discrepancies between the conventional error model and our more realistic approach, underscoring the limitations of the former in practical applications.

Quantum reading is one of application protocols of entanglement. This protocol uses entanglement for reading of a digital memory such as a CD or DVD. O. Hirota showed that in a noiseless environment, quantum reading using a quasi-Bell state that has maximum entanglement is error free. Moreover, K. Kato and O. Hirota considered equal losses for amplitudes of modes A and B of this state in determining energy-loss effects. However, in real settings, the loss associated with the amplitude of mode B is greater than that of mode A. Therefore, we consider non-symmetric loss and its effect on quantum reading using a quasi-Bell state. In this paper, we show the analytical solution of the error probability in this case, and investigate the amplitude of mode A that minimizes the error probability when the amplitude of mode B is fixed. Moreover, we consider the robustness against alignment mismatch.

In quantum communication theory, group covariant signals are important and useful when we consider the minimization problem of the error probability or the maximization problem of the mutual information. However, in practical applications, there are important non-symmetric signals such as amplitude shift keying or quadrature amplitude modulation signals. To manage this situation, we have proposed a symmetrization method of non-symmetric pure-state signals by using coding. In this paper, we consider to apply the symmetrization method to mixed-state signals and give a necessary condition of mixed-state signals to apply the method. Then, we present examples of mixed-state signals to which the symmetrization method can be applied.

In quantum communications, the performance of a quantum measurement with phase noise has not widely been discussed. In this paper, we focus on error performance, as well as robustness, in a comparison with a classical measurement using multiple phase-shift keying when phase noise is generated. With increasing signal dimension, we analyze numerically the trend in robustness in terms of the error performance and the gain in robustness.

We study the realization of a 2-D positive operator-valued measure (POVM) by local operations and classical communication (LOCC). We derive that any POVM on a 2-D Hilbert space in which each party's space is finite dimensional can be realized by one-way LOCC. This implies that any optimal discrimination of quantum states spanning such a 2-D Hilbert space is possible by one-way LOCC, regardless of the optimality criterion used and how entangled the states are.

We study an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average success probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman-Pearson strategy. We show that for any generalized quantum state discrimination problem, there is a corresponding minimum error discrimination problem sharing the same optimal measurement. We propose an approach in which the optimal measurement is obtained by solving the corresponding minimum error discrimination problem, and clarify the relationship between optimal solutions to the original and the corresponding problems, with which one can obtain an optimal solution to the original problem in some cases. Moreover, as an example of application of our approach, we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems.

We derive some properties of minimum-error measurements for mixed quantum state signals where a density operator itself has a certain symmetry. In the first case, we show that if there exists a regular normal operator that commutes with each density operator of mixed state signals, then there exists an optimal measurement that consists of detection operators expressed as the direct sum of positive operators with supports in the eigenspaces of the regular normal operator. In the second case, we show that for abelian geometrically uniform state signals, if a matrix which represents one of the signals in a certain basis has all real elements, then the matrix which represents the corresponding detection operator of an optimal measurement in that basis also has all real elements. In addition, we discuss some examples of applications of these properties and derive analytical solutions of optimal measurements for special cases.

A formula of channel matrix for linear codes over Zmis presented. m-ary PSK coherent-states are used as letter states and the square-root measurement (SRM) is used as a decoding. First, arbitrary linear codes over Zmare shown to group covariant. Then the formula of channel matrix is derived by generalizing [T.S. Usuda, S. Usami, I. Takumi, and M. Hata, Phys. Lett. A305, pp.125-134, (2002)]. Furthermore, the usefulness of the formula is considered.

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.