We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic st...We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic states are quantum resources in the stabilizer formalism of quantum computation.SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations,quantum state tomography,and quantum cryptography,etc.In this work,we study group frames constructed from some prominent magic states,and further investigate their applications.Our method exploits the orbit of discrete Heisenberg-Weyl group acting on an initial fiducial state.We quantify the distance of the group frames from SIC-POVMs and MUBs,respectively.As a simple corollary,we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states,analogous to the well-known SIC-POVM fiducial states.We present an intuitive and direct construction of MUB fiducial states via quantum T-gates,and demonstrate that for the qubit system,there are twelve MUB fiducial states,which coincide with the H-type magic states.We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation.We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.展开更多
Based on the frame structure of intermediate data rate （IDR） modem for satellite communication, a new method for searching frame synchronization called group frame synchronization is proposed. At the same time, a ca...Based on the frame structure of intermediate data rate （IDR） modem for satellite communication, a new method for searching frame synchronization called group frame synchronization is proposed. At the same time, a candidate scheme in the classical frame synchronization and two candidate schemes in the group frame synchronization are presented, and the circuits for each scheme are designed in order to abstract the frame alignment signals from received data. Their implementation complexity and performances are also computed and given. Based on the analysis and performance comparison, a reasonable scheme is chosen and then verified through software simulation and hardware impletentation.展开更多
Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜...Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.展开更多
自联合国国际搜索与救援咨询团(The International Search and Rescue Advisory Group,简称INSARAG)成立30多年来,通过不断总结巨灾国际救援经验,形成了一套覆盖国际救援准备阶段、行动阶段到撤离阶段的国际救援全流程全要素的协调工作...自联合国国际搜索与救援咨询团(The International Search and Rescue Advisory Group,简称INSARAG)成立30多年来,通过不断总结巨灾国际救援经验,形成了一套覆盖国际救援准备阶段、行动阶段到撤离阶段的国际救援全流程全要素的协调工作机制,并通过出台一系列的指南、指导性文件和推荐性技术文件,规范救援能力和队伍建设,强化国际救援协调和现场救援的效率。该文系统介绍了INSARAG标准和技术文件组成体系架构,并阐述了各标准及技术文件的出台背景、主要内容及对中国的搜救队伍建设的推动作用,并讨论其对我国灾害救援工作的启示与借鉴意义。展开更多
基金supported by the National Key R&D Program of China,Grant No.2020YFA0712700the National Natural Science Foundation of China‘Mathematical Basic Theory of Quantum Computing’special project,Grant No.12341103。
文摘We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic states are quantum resources in the stabilizer formalism of quantum computation.SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations,quantum state tomography,and quantum cryptography,etc.In this work,we study group frames constructed from some prominent magic states,and further investigate their applications.Our method exploits the orbit of discrete Heisenberg-Weyl group acting on an initial fiducial state.We quantify the distance of the group frames from SIC-POVMs and MUBs,respectively.As a simple corollary,we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states,analogous to the well-known SIC-POVM fiducial states.We present an intuitive and direct construction of MUB fiducial states via quantum T-gates,and demonstrate that for the qubit system,there are twelve MUB fiducial states,which coincide with the H-type magic states.We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation.We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.
文摘Based on the frame structure of intermediate data rate （IDR） modem for satellite communication, a new method for searching frame synchronization called group frame synchronization is proposed. At the same time, a candidate scheme in the classical frame synchronization and two candidate schemes in the group frame synchronization are presented, and the circuits for each scheme are designed in order to abstract the frame alignment signals from received data. Their implementation complexity and performances are also computed and given. Based on the analysis and performance comparison, a reasonable scheme is chosen and then verified through software simulation and hardware impletentation.
文摘Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.
文摘自联合国国际搜索与救援咨询团(The International Search and Rescue Advisory Group,简称INSARAG)成立30多年来,通过不断总结巨灾国际救援经验,形成了一套覆盖国际救援准备阶段、行动阶段到撤离阶段的国际救援全流程全要素的协调工作机制,并通过出台一系列的指南、指导性文件和推荐性技术文件,规范救援能力和队伍建设,强化国际救援协调和现场救援的效率。该文系统介绍了INSARAG标准和技术文件组成体系架构,并阐述了各标准及技术文件的出台背景、主要内容及对中国的搜救队伍建设的推动作用,并讨论其对我国灾害救援工作的启示与借鉴意义。
