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.
The film market during the Spring Festival in the year of the snake can be described as “YOLO”(which means hot),with six films are released simultaneously, including Ne Zha 2, Detective Chinatown 1900, Boonie Bears:Future Reborn,Operation Hadal, Creation of the Gods II:Demon Force (hereinafter referred to as Creation of the Gods II) and Legends of The Condor Heroes:The Gallants.These movies show a variety of national and patriotic feelings and traditional culture. Among them, Ne Zha 2 has been constantly breaking record since the box office exceeded RMB 14 billion.
On December 7,2024,the People’s Literature Publishing House hosted the grand launch event for the Harry Potter(25th Anniversary Edition)at the Beijing Dahua City Performing Arts Center.With the theme“The Magic Lives On,”the event featured three parts:a guest panel discussion,fan sharing,and interactive activities.Zang Yongqing,member of the Party Leadership Group of China Publishing Group Corporation and vice general manager of China Publishing&Media Holdings Co.,Ltd.,delivered the opening remarks.
One day,Miriam got a letter along with a watermelon seed from U ncle Esai.The letter said:Miriam,This is a magic seed for you.Plant it,and it will grant1you three wishes.Remember to be patient:the world has its own rhythm.Uncle Esai Miriam thought,"A magic seed?M aybe it's Uncle Esai's joke,but why not have a try?"She planted the seed in the yard,and made her first wish,"I want the watermelon to grow as big as a mountain."
By combining experimental α-decay energies and half-lives, the α-particle preformation factor for nuclei around neutron magic numbers N of 126, 152, and 162 were extracted using the two-potential approach. The nuclei around the shell closure were more tightly bound than adjacent nuclei. Additionally, based on the WS4 mass model (Wang et al., Phys. Lett.B 734, 215 (2014)), we extended the two-potential approach to predict the α-decay half-lives of nuclei around N values of178 and 184 with Z of 119 and 120. We believe that our findings will serve as guidelines for future experimental studies.
Ming LiChu-Xin ChenLan-Fang XiaoYi ZhangSong LuoXiao-Hua Li
