Group frames via magic states with applications to SIC-POVMs and MUBs  

作　　者：Lingxuan Feng Shunlong Luo 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Communications in Theoretical Physics》2025年第1期41-53,共13页理论物理通讯(英文版)

基　　金：supported by the National Key R&D Program of China,Grant No.2020YFA0712700;the National Natural Science Foundation of China‘Mathematical Basic Theory of Quantum Computing’special project,Grant No.12341103。

摘　　要：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.

关 键 词：Group frames magic states MUBs SIC-POVMs quantum T-gates 

分 类 号：O413[理学—理论物理]