Quantum Fourier analysis.
Where this comes from
- Record sourced from PubMed, PMID 32354991.
- Also identified by DOI 10.1073/pnas.2002813117 and PMC identifier 7245120.
- Licence recorded as CC BY-NC-ND.
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Abstract
Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform F, as a map between suitably defined [Formula: see text] spaces, leading to an uncertainty principle for relative entropy. We cite several applications of quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a topological inequality, and we outline several open problems.