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.

Short cycle test pattern can sensitize target paths deterministically and periodically in short interval. It is useful to apply the short cycle test pattern for accelerating scan-based delay measurement. This paper presents the deterministic scan-based online delay measurement using short cycle test pattern for short measurement time. Applying short cycle test pattern to scan-based online delay measurement drastically reduces the time required for iterative path sensitizations, which reduces the measurement time. It makes scan-based critical path delay measurement practical for DFS, DVS, and prediction of aging. Evaluation reveals that the cycle of the path sensitization using short cycle test pattern is 9.1 clocks on average. The average of the measurement time is 28.6 % of normal scan-based measurement. The data volume is 59.1 % of normal scan-based measurement on average. The area overhead is 19.0 % of full scan design.

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.

The necessary and sufficient conditions for the minimax strategy of a finite number of decisions in quantum signal detection are derived in the case that the average Bayes cost is used as a quality function. This is a simple extension of the result of Hirota and Ikehara [1]. Applying the necessary and sufficient conditions, a closed-form expression of the minimax strategy for binary pure state signal is shown. Furthermore, the minimax strategy for a discrimination problem of the quasi-Bell states is considered. In this case, the square-root measurement consisting of the quasi-Bell states yields the minimax strategy.

A certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals. This correspondence shows that the square-root measurement gives the optimal measurement for such a class of mixed states.

We analyze the performance of the error probability and the mutual information for quadrature amplitude modulation (QAM) and phase-shift keying systems based on quantum detection theory. It is shown that the quantum receiver called square root measurement gives about 5.7 dB improvement in power in comparison with the classical one. Furthermore, we show that the quantum QAM system can achieve the same reliability as the conventional intensity modulation-direct detection (IM-DD) system with almost equal power, compressing the required bandwidth, while the reliability is degraded in general.