Quantum Fourier analysis
Abstract
Classical Fourier analysis, discovered over 200 years ago, remains a cornerstone in understanding almost every field of pure mathematics. Its applications in physics range from classical electromagnetism to the formulation of quantum theory. It gives insights into chemistry, engineering, and information science, and it underlies the theory of communication. Quantum Fourier analysis extends this perspective. It yields insights and inequalities associated with uncertainty principles for quantum symmetries. In this paper, we introduce this mathematical subject, we show how it can solve some theoretical problems, and we give some applications to quantum physics with bounds on entropy and the analysis of quantum entanglement. We believe that quantum Fourier analysis, now in its infancy, will have significant future impact.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 30, 2020
- Source ID
- 10.1073/pnas.2002813117
Entities
People
- Arthur Jaffe
- Chunlan Jiang
- Jinsong Wu
- Yunxiang Ren
- Zhengwei Liu
Organizations
- Army Research Office
- Harbin Institute of Technology
- Harvard University
- Hebei Normal University
- National Natural Science Foundation of China
- Templeton Religion Trust
- Tsinghua University