级联光束分离器的纠缠特性及其应用  

Entanglement properties of multi-cascaded beamsplitter and its applications

作　　者：贾芳 张魁正[1] 胡银泉 张浩亮 胡利云 范洪义 Jia Fang;Zhang Kui-Zheng;Hu Yin-Quan;Zhang Hao-Liang;Hu Li-Yun;Fan Hong-Yi(Key Laboratory of Optoelectronic and Telecommunication,Jiangxi Normal University,Nanchang 330022,China;Department of Material Science and Engineering,University of Science and Technology of China,Hefei 230026,China;Center for Quantum Science and Technology,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学,江西省光电子与通信重点实验室,南昌330022 [2]中国科技大学材料科学与工程系,合肥230026 [3]江西师范大学,量子科学与技术中心,南昌330022

出　　处：《物理学报》2018年第15期260-268,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号：11664017,11464018,11264018); 江西省杰出青年人才项目(批准号：20171BCB23034); 江西省学位与研究生教育教学改革研究项目(批准号：JXYJG-2013-027)资助的课题

摘　　要：光束分离器是一个具有广泛应用的线性光学器件,它在非经典量子态特别是纠缠态的制备中具有重要作用.基于单个光束分离器的表象表示,本文进一步考察多个级联光束分离器的纠缠特性,特别是结合有序算符内的积分技术推导了级联光束分离器的正规乘积、紧指数表示及级联算符的表象表示.作为应用,本文利用两个级联光束分离器获得了量子力学表象及其Schmidt分解,并结合量子条件测量制备了qubit态的叠加态.本文的研究方法已被直接推广至多个光束分离器级联情况,相关研究内容为多模纠缠态、多模qubit态的制备提供了一种有效的途径,且为由光束分离器组成的线性器件系统总作用的算符正规乘积及其紧指数表示提供了一般方法.Beam splitter, as a kind of linear optics instruments, has many applications such as in quantum optics and quantum information, including the preparation of nonclassical quantum states and entangled state representation. In Heisenberg picture, on the one hand, the relation of input-output of beam splitter can be easily obtained. Especially for the multicascaded beam-splitters, the input-output relation can also be directly obtained by the input-output relation of single beam splitter. On the other hand, we often need to calculate the probabilities of detecting photon number in many cases, thus we need to turn into Schr？dinger picture for simplifying our calculation. Based on the equivalence between both pictures, the relation between transformation matrixes connecting these two pictures is derived. That is to say,the transform matrix corresponding to the Schr？dinger picture can be obtained by transposing the transform matrix in Heisenberg picture. This concise relation constructs a bridge connecting two pictures and simplifies our calculation in the Schr？dinger picture rather than step by step. Using the relation between transform matrixes of both pictures and combining the technique of integration within ordered product of operator, we further consider the coordination representation, normally ordering form and exponential expression of single beam-splitter. Then we further examine the coordination representation, normally ordering form and exponential expression of two-cascaded beam-splitters. As a generalization, the method is extended to the case of multi-cascaded beam-splitters. These investigations provide an effective way to prepare multi-mode entangled states and qubit states. In addition, a general method is shown of obtaining the total operator and its normally ordering form as well as Schmidt decomposition of the linear systems consisting of beam-splitters. As applications, 2-cascaded beam-splitters is used to generate a new quantum mechanics representation and prepare the qubit states with the h

关 键 词：光束分离器级联算符 多模纠缠态表象 有序算符内积分技术 Schmidt分解 

分 类 号：O413[理学—理论物理]