题  目: Zauner’s Conjecture: Fiducial States in Vector Spaces

时间：2023年12月1日9:00

地点：藕舫楼724

报告人: 骆顺龙研究员

中国科学院数学与系统科学研究院

应用数学研究所

主持人：张志超

摘要: In the stabilizer formalism of quantum theory, stabilizer states serves as classical objects, and non-stabilizer states (magic states) are resource for genuine quantum computation. In the paradigm of quantum measurement, symmetric informationally complete positive operator valued measures (SICs) play a prominent role due to their structural symmetry and remarkable features. However, their existence in all dimensions, although strongly supported by a plethora of theoretical and numerical evidence, remains an elusive open problem (Zauner's conjecture). A standard method for constructing SICs is via the orbit of Heisenberg-Weyl group on a fiducial state. A natural question arises as the relation between stabilizer states and fiducial states. In this talk, we connect them by showing that they are on two extremes with respect to the p-norm of characteristic functions of quantum states. This not only reveals a simple path from stabilizer states to SIC fiducial states which shows in a quantitative fashion that they are as far away as possible from each other, but also provides a simple reformulation of Zauner's conjecture. A convenient criterion for non-stabilizerness and some open problems are also presented.

简介: 骆顺龙, 1989年获上海交通大学学士学位, 1995年获武汉大学博士学位。现任中国科学院数学与系统科学研究院应用数学研究所研究员, 所长, 量子计算与量子信息处理研究中心主任。曾应邀在第八届国际工业与应用数学大会作一小时报告 (2015)。主要从事概率统计﹑量子论和信息论研究。