Hun-Hee Lee——Quantum information and abstract harmonic analysis


题目Quantum information and abstract harmonic analysis

报告人Hun-Hee Lee(Seoul National University)



摘要In quantum information theory we are interested in quantum states, i.e. a positive operators with trace 1. Operators are, in general, difficut to handle, so that we prefer to find associated functions possibly keeping all the information intact. This is what quantum researchers have been doing when they investigate n-mode Bosonic quantum state under the name of characteristic function and Wigner function. In this talk we will see that this state <--> characteristic function correspondence is nothing but a twisted Fourier transform on the group R^{2n}, where we may possibly apply abstract harmonic analysis tools for understanding certain quantum states. We will also examine other examples of quantum systems where we can apply this new perspective including the Fermionic system. Finally, we will re-examine a result by R. Hudson from '70's in an abstract harmonic analysis point of view with possible extension to other cases.

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