报告名称：Quantum KKL, Talagrand and Friedgut’s theorems

主讲人：Haonan Zhang (IST Austria)

时间：10月06日（星期四）20:30--22:00

地点：线上Zoom会议

联系人：常帆 cf25264@163.com

报告摘要：The KKL theorem is a fundamental result in Boolean analysis, saying that any Boolean function has an influential variable. Two related results are Talagrand’s inequality which implies the KKL theorem, and Friedgut’s theorem on juntas. Montanaro and Osborne proposed a quantum extension of Boolean functions. In this context, many classical results have been extended to the quantum setting, such as Talagrand’s inequality. However, this quantum Talagrand’s inequality does not seem to derive a KKL theorem in the quantum setting. So a quantum version of the KKL theorem seems to be missing, as conjectured by Montanaro and Osborne. In this talk, I will present an alternative answer to this question. We prove that every balanced quantum Boolean function has a geometrically influential variable. This is based on a quantum analogue of a variant of Talagrand’s inequality which we prove using recently studied hypercontractivity and gradient estimates. We also prove Friedgut’s junta Theorem in the quantum setting that has applications in the learnability of quantum observables. This is based on joint work with Cambyse Rouzé (TUM) and Melchior Wirth (IST Austria).

个人简介：Haonan Zhang is currently a postdoc at IST Austria. His research interests are noncommutative analysis and applications.

邀请人：王光辉教授