The Necessary and Sufficient Conditions When Global and Local Fidelities Are Equal.

In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system A⊗B is always less than or equal to the quantum fidelity between the states in subsystem A alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system A⊗B and subsystem A, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results.

Health to Eat: A Smart Plate with Food Recognition, Classification, and Weight Measurement for Type-2 Diabetic Mellitus Patients' Nutrition Control.

The management of type 2 diabetes mellitus (T2DM) is generally not only focused on pharmacological therapy. Medical nutrition therapy is often forgotten by patients for several reasons, such as difficulty determining the right nutritional pattern for themselves, regulating their daily nutritional patterns, or even not heeding nutritional diet recommendations given by doctors. Management of nutritional therapy is one of the important efforts that can be made by diabetic patients to prevent an increase in the complexity of the disease. Setting a diet with proper nutrition will help patients manage a healthy diet. The development of Smart Plate Health to Eat is a technological innovation that helps patients and users know the type of food, weight, and nutrients contained in certain foods. This study involved 50 types of food with a total of 30,800 foods using the YOLOv5s algorithm, where the identification, measurement of weight, and nutrition of food were investigated using a Chenbo load cell weight sensor (1 kg), an HX711 weight weighing A/D module pressure sensor, and an IMX219-160 camera module (waveshare). The results of this study showed good identification accuracy in the analysis of four types of food: rice (58%), braised quail eggs in soy sauce (60%), spicy beef soup (62%), and dried radish (31%), with accuracy for weight and nutrition (100%).