题目：Sample-optimal tomography of quantum states
主讲人：俞能昆（悉尼科技大学，高级讲师）
日期：2018年11月30日（星期五）
时间：上午10:30 - 11:30
地点：数据科学与jbo竞博电竞官方网站 A201
主持：李绿周副教授
摘要：It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error ε in trace distance required O(dr2/ε2) copies for a d-dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O(dr/δ)ln(d/δ) copies of ρ to error δ in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr/ε2)ln(d/ε)) copies suffice to achieve error ε in trace distance. We also prove that for independent (product) measurements, Ω(dr2/δ2)/ln(1/δ) copies are necessary in order to achieve error δ in infidelity. For fixed d, our measurementcan be implemented on a quantum computer in time polynomial in n.
个人介绍：俞能昆，悉尼科技大学高级讲师，分别于 2008 年和 2013 年于清华大学计算机科学与技术系取得本科和博士学位，主要研究方向为量子计算和量子信息。目前已经在 STOC，Physical Review Letters，IEEE Transaction on Information Theory 等会议和期刊发表多篇论文。