From the basic measurement parameters, the Pythagorean triangle of the right triangle is the core measurement, and the corresponding angle is the target of trigonometric geometry. Generalized to complex functions, the argument angle corresponding to the complex conjugate operator is a negative angle. Although the complementary angles of a right triangle (angle + complementary angle = 90 degrees), play a complementary role in geometric analysis. However, this type of complementary measurement effect is completely ignored in the traditional complex variable function of the quantum measurement system.

In the conjugate system, the complementary effect is the result of the conjugate operator that plays the core role of local/global correlation. The extended vector description structure formed by the expansion mode of the complementary angle geometric operator forms a new conjugate complex vector system. Starting from the basis of conjugate complex functions to support the comprehensive description of various hyper complex dynamic systems.

Due to the expanded space of the conjugate operator, it can effectively support the quantum entanglement that appears as a series of paradoxes in the classical quantum system with a sufficient large capacity. The conjugate structured expanded logical-mathematical description system can complete the elusive quantum entanglement effect to support the ground.

It is a characteristic of this basic research to find flaws in classical theories based on logical and mathematical theories such as vector logic/conjugate measurement/visualization of conjugate complex functions, which are the basis of quantum measurement. How many people agree depends on whether the series of predictions proposed in the monograph on conjugate quantum optics can be denied or confirmed by precise experiments. From the feature similarity comparison, the simulation calculation results given are highly consistent with the latest quantum entanglement measurement effects. From the measurement models, the three types of quantum entanglement measurement models given each have prototypes and can be directly verified.

Just use this article to inspire others! We look forward to top experts in the fields of international logical foundations, mathematical foundations, complex functions, Hilbert space, quantum mechanics, quantum gravity, quantum measurement, theoretical physics, quantum optics, quantum information, quantum entanglement, quantum measurement and other fields to discuss conjugate structures. The core and series of inferences are provided, and the basic theory and precise measurement evidence to support/deny are given.