题目: Phase group category of bimodule quantum channels

报告人：清华大学 吴劲松教授

时间：2024年12月09日19:00-20:00

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https://meeting.tencent.com/dm/sCFEkLTqlQ9T

腾讯会议：758-737-955

会议密码：1209

摘要: In this talk, we will investigate the quantum channel on a von Neuamnn algebras M preserving a von Neumann subalgebra N, namely N-N-bimodule unital completely positive map. By introducing the relative irreducibility of a bimodule quantum channel, we show that its eigenvalues with modulus 1 form a finite cyclic group, called its phase group. Moreover, the corresponding eigenspaces are invertible N-N-bimodules, which encode a categorification of the phase group. When N⊂Mis a finite-index irreducible subfactor of type II1, we prove that any bimodule quantum channel is relative irreducible for the intermediate subfactor of its fixed points. In addition, we can reformulate and prove these results intrinsically in subfactor planar algebras without referring to the subfactor using the methods of quantum Fourier analysis.

简介：吴劲松，现就职北京雁栖湖应用数学研究院，研究员。中科院数学与系统科学研究院博士学历。曾就职于中国科学技术大学，哈尔滨工业大学等。主要研究方向为泛函分析，算子代数以及其在量子信息等领域的应用，是量子傅立叶分析发起人之一。主持和参与多项国家自然科学基金项目。主要成果发表在国际著名期刊如PNAS, Adv Math, Comm Math Phys, J Func Anal, Sci China Math等。