Quantum entropy and central limit theorem.

We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a "maximal entropy principle in DV systems." We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a "second law of thermodynamics for quantum convolutions." We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state, and show this converges to its MS. The rate of convergence is characterized by the "magic gap," which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.

Sub-nanometre quality X-ray mirrors created using ion beam figuring.

Ion beam figuring (IBF) is a powerful technique for figure correction of X-ray mirrors to a high accuracy. Here, recent technical advancements in the IBF instrument developed at Diamond Light Source are presented and experimental results for figuring of X-ray mirrors are given. The IBF system is equipped with a stable DC gridded ion source (120 mm diameter), a four-axis motion stage to manipulate the optic, a Faraday cup to monitor the ion-beam current, and a camera for alignment. A novel laser speckle angular measurement instrument also provides on-board metrology. To demonstrate the IBF system's capabilities, two silicon X-ray mirrors were processed. For 1D correction, a height error of 0.08 nm r.m.s. and a slope error of 44 nrad r.m.s. were achieved. For 2D correction over a 67 mm × 17 mm clear aperture, a height error of 0.8 nm r.m.s. and a slope error of 230 nrad r.m.s. were obtained. For the 1D case, this optical quality is comparable with the highest-grade, commercially available, X-ray optics.

Mixed stitching interferometry with correction from one-dimensional profile measurements for high-precision X-ray mirrors.

This work presents a mixed stitching interferometry method with correction from one-dimensional profile measurements. This method can correct the error of stitching angles among different subapertures using the relatively accurate one-dimensional profiles of the mirror, e.g., provided by the contact profilometer. The measurement accuracy is simulated and analyzed. The repeatability error is decreased by averaging multiple measurements of the one-dimensional profile and using multiple profiles at different measurement positions. Finally, the measurement result of an elliptical mirror is presented and compared with the global algorithm-based stitching, and the error of the original profiles is reduced to one-third. This result shows that this method can effectively suppress the accumulation of stitching angle errors in classic global algorithm-based stitching. The accuracy of this method can be further improved by using high-precision one-dimensional profile measurements such as the nanometer optical component measuring machine (NOM).

XDMOM: A Real-Time Moving Object Detection System Based on a Dual-Spectrum Camera.

A low-cost and power-efficient video surveillance system, named XDMOM, is developed for real-time moving object detection outdoors or in the wild. The novel system comprises four parts: imaging subsystem, video processing unit, power supply, and alarm device. The imaging subsystem, which consists of a dual-spectrum camera and rotary platform, can realize 360-degree and all-day monitoring. The video processing unit uses a power-efficient NVIDIA GeForce GT1030 chip as the processor, which ensures the power consumption of the whole system maintains a low level of 60~70 W during work. A portable lithium battery is employed to supply power so that the novel system can be used anywhere. The work principle is also studied in detail. Once videos are recorded, the single-stage neural network YOLOv4-tiny is employed to detect objects in a single frame, and an adaptive weighted moving pipeline filter is developed to remove pseudo-targets in the time domain, thereby reducing false alarms. Experimental results show that the overall correct alarm rate of the novel system could reach 85.17% in the daytime and 81.79% at night when humans are monitored in real outdoor environments. The good performance of the novel system is demonstrated by comparison with state-of-the-art video surveillance systems.