Kenji Nakahira

Generalized quantum state discrimination problems

We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a fixed rate of inconclusive results. Our approach can deal with any problem in which each of the objective and constraint functions is formulated by the sum of the traces of the multiplication of a Hermitian operator and a detection operator. We first derive dual problems and necessary and sufficient conditions for an optimal measurement. We also consider the minimax version of these problems and provide necessary and sufficient conditions for a minimax solution. Finally, for optimization problem having a certain symmetry, there exists an optimal solution with the same symmetry. Examples are shown to illustrate how our results can be used.

A New Image Restoration Technique for SEM

Abstract This paper proposes a new fast and effective method of image restoration to improve the resolution of SEM images. In our approach, image resolution is improved by deconvolution with the point spread function modeled as the intensity distribution of the electron beam at the specimens surface. The beam intensity distribution under each imaging condition is estimated by electro-optical simulation to achieve high resolution. We propose an iterative technique for the deconvolution process with a cost function where the restored image at each iteration can be compared with the original image more directly. A wavelet shrinkage denoising algorithm was applied to efficiently suppress noise amplification in noisy images, The empirical results demonstrate the outstanding improvements in both resolution and noise suppression. The proposed iterative method also speeds up deconvolution by about 3 to 50 times more than the conventional Richardson-Lucy method.

Finding Optimal Solutions for Generalized Quantum State Discrimination Problems

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.

Realizing a Two-Dimensional Positive Operator-Valued Measure by Local Operations and Classical Communication

We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a twodimensional Hilbert space in which each party’s space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.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.

A novel approach for scanning electron microscopic observation in atmospheric pressure

Atmospheric scanning electron microscopy (ASEM) for observing samples at ambient atmospheric pressure is introduced in this study. An additional specimen chamber with a thin membrane allowing electron beam propagation is inserted in the main specimen chamber. Close proximity of the sample to the membrane enables the detection of backscattered electrons (BSEs) sufficient for imaging. A probability analysis of the un-scattered fraction of the incident electron beam and the beam profile further supports the feasibility of atmospheric SEM imaging over a controlled membrane-sample distance. An image enhancement method based on the analysis is introduced for the ASEM.

Upper and lower bounds on optimal success probability of quantum state discrimination with and without inconclusive results

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds are evaluated through numerical experiments.

Reduction of Electron Scattering Image Blur for Atmospheric Scanning Electron Microscopy

Recently, methods for observing samples under atmospheric pressure in a scanning electron microscope (SEM) have been reported by some investigators. We proposed a novel atmospheric SEM (ASEM) technique for observing samples which are present in ambient air conditions but are separated from the membrane [1]. In our system, the environment around the sample can be kept in ambient air conditions (Fig. 1(a)). While wet materials is clearly observed without direct sample membrane contact at an optimized distance, typical atmospheric SEM image taken in atmosphere is more blurred compared to conventional SEM image taken in vacuum condition. The reason why ASEM images looks like “blurred” is because electron beam is scattered by electron scattering region shown in Fig. 1(b). In order to reduce the electron scattering effect, some methods utilizing light element gas [2] or additional vacuum pump to reduce pressure [1] (10 4 ~10 5 Pa) have been developed. A typical atmospheric SEM image is shown in Fig. 1(c). Brightness of point B is brighter than that of point A, although the edge of number “9” is clear. The image gives us a consideration that the profile of electron beam arriving at sample is estimated as sum of scattered and un-scattered electrons beam. As a result, the image in Fig. 1(c) seems to be blurred. Based on the consideration, we develop an image enhancement algorism for ASEM (electron scattering corrector: ES-Corrector). By using this algorism, blurring created by scattered electrons in ASEM image can be improved after detection of SEM image. Figure 2 shows SEM images of Cu mesh (Fig. 2(a)(b)) taken in atmospheric pressure. Figure 2(c) and (d) are restored images using ES-Corrector. The images show great improvements in clarity and edge sharpness than the observed images. The microstructures on Cu mesh observed in Fig. 2(c) and (d) are compatible to those in SEM images taken in vacuum Fig. 2(e) and (f). Figure 3 shows SEM images of a filter paper (Fig. 3(a)), renal glomerulus without metal staining (Fig. 2(b)), a leaf surface of the Japanese radish(Fig. 3(c)), and blood cells fixed with 1% glutaraldehyde and immune-stained with gold particles (Fig. 3(d)) taken in atmospheric pressure at room temperature. Figure 3(a)-(h) is the original and restored images. The images show great improvements in clarity and edge sharpness than the observed images. It has been shown that the ES-Corrector algorism to reduce effect of scattered electrons from ASEM image can improve image quality.

A generalized Dolinar receiver with inconclusive results

We investigate the implementation of a measurement for binary optical coherent states that minimizes the error probability with a fixed rate of an inconclusive result. We find that the optimal measurement for binary optical coherent states with any probability of an inconclusive result can be implemented using only a beam splitter, a local coherent light source, a photon detector, and a feedback circuit, even though the measurement is generally not projective.

Minimum-Error Discrimination Between Self-Symmetric Mixed Quantum State Signals

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.