K. Nakahira et al. introduced iterative algorithms to determine the optimal quantum detection for general quantum state signals under the minimum-error and minimax criteria. In this paper, we aim to modify these algorithms, assuming that the signal states are pure and linearly independent. We demonstrate that the algorithms can be modified using the properties of the Gram matrix of linearly independent pure states. This modification eliminates the need to compute the inverse of the square root of the weighted Gram matrix, which is required in the original algorithms, thereby simplifying their implementation.

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 prototype bat-like sonar system has been developed by implementing some of the bat techniques for interpreting sonar signals and mimicking their sensor configuration. The optimum method for estimating time-of-flight from the frequency-modulated echoes is correlation detection. In the field of photon correlation spectroscopy, a hardware digital correlator is employed to process the correlation function in real time. The paper presents an application of hardware digital correlators, implemented on a programmable logic device, as sonar signal processing systems for obstacle localization.