噪声环境中量子Fisher信息的几何表示  

Geometric representation of quantum Fisher information in noisy environment

作　　者：严凯[1] 谢燕青[1] 黄雨梦 郝翔[1] YAN Kai;XIE Yanqing;HUANG Yumeng;HAO Xiang(School of Mathematics and Physics,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2018年第4期28-33,55,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(61875145);江苏省自然科学基金项目(BK20170376);"十三五"重点学科建设项目(20168765);江苏省研究生创新工程教改项目(JGLX15-150);苏州科技大学研究生教改项目(SKJG15_06)

摘　　要：从数学几何角度研究了噪声通道中相位参数估计的量子Fisher信息。对于单量子态,参数估计精度可用态Bloch矢量在XY平面上的投影长度定量刻画。对于多体广义GHZ量子纠缠态,量子Fisher信息也可以用一个等效密度算子的Bloch矢量来描述。以腔量子动力学系统为研究对象,考虑一种典型的退振幅噪声通道,发现如果原子系统和环境场中心频率存在失谐量,环境与耦合增加会抑制量子Fisher信息的衰减,Bloch矢量也会保持在球体赤道表面振荡。相比于直积态,N个初始纠缠的广义GHZ态的量子Fisher信息会得到N倍的提高,但是其衰减也会加快。From the viewpoint of the geometric representation,we investigated the quantum Fisher information with respect to phase parameter in noisy channels.For single qubit,the value of quantum Fisher information can be characterized by the projecting length of the Bloch vector on XY plane.For a generalized Greenberger-Horne-Zeilinger(GHZ)entangled state,its quantum Fisher information can also be described by the Bloch vector of the equivalent density operator.The open atoms in Cavity QED was considered and modeled by the typical amplitude damping channel.The detuning between the transition frequency of atoms and central frequency of the environment spectrum can suppress the decay of quantum Fisher information.And the oscillations of the Bloch vectors are round the equator.Compared with the product state,the GHZ entangled state with N particle can enhance quantum Fisher information N times.Meanwhile the QFI decays more quickly.

关 键 词：量子参数估计 量子Fisher信息 Bloch矢量 腔量子动力学系统 

分 类 号：O441.4[理学—电磁学]