中科院数学与系统科学研究院
数学研究所
学术报告会
报告人：俞能昆 博士（加拿大滑铁卢大学量子计算研究所）
题 目：Separability of Bosonic Systems
时 间：05.13(星期三), 10:00--11:00
地 点：数学院南楼N208室
Abstract: We study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive Matrices" is drawn. Such connection is employed to demonstrate that multi-qubit quantum states with Dicke states being its eigenvectors is separable if and only if two related Hankel matrices are positive semidefinite. By employing this criterion, we are able to show that such state is separable if and only if it's partial transpose is non-negative, which confirms the conjecture in [Wolfe, Yelin, Phys. Rev. Lett. (2014)]. Then, we present a class of bosonic states in d⊗d system such that for general d, determine its separabilityNP-hard although verifiable conditions for separability is easily derived in case d=3,4.
