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Abstract: Particle accelerators have achieved remarkable progress over the last several decades. Since the accelerator supported us in answering fundamental question36s to understand the universe, its impact was broadened to other science. Nowadays, accelerators are adopted to assist medical therapy, industries, and even the humanities. One of the keys to enabling such a wide variety of applications is beam manipulation. Accelerators optimize a particle beam to maximize the performance of their applications, and beam manipulations have made such optimizations. I will start with several conventional and newly developed manipulation methods and tools. The main focus of the talk will be recent research on arbitrary correlation generation and its applications.