| Majorana stellar representation for mixed-spin (s, 1/2) systems |
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| 作者姓名： | 苏玉国 姚飞 梁宏宾 车彦明 傅立斌 王晓光 |
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| 作者单位： | Zhejiang Province Key Laboratory of Quantum Technology and Device;National Laboratory of Science and Technology on Computational Physics |
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| 基金项目： | Project supported by the National Key Research and Development Program of China(Grant Nos.2017YFA0304202 and 2017YFA0205700);the National Natural Science Foundation of China(Grant No.11875231);the Fundamental Research Funds for the Central Universities,China(Grant No.2018FZA3005). |
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| 摘 要： | By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s?1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s?1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s?1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.
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| 关 键 词： | Majorana’s stellar representation Bloch sphere high-dimensional projective Hilbert space mixedspin |
Majorana stellar representation for mixed-spin (s, 1/2) systems |
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| Yu-Guo Su,Fei Yao,Hong-Bin Liang,Yan-Ming Che,Li-Bin Fu,Xiao-Guang Wang.Majorana stellar representation for mixed-spin (s, 1/2) systems[J].Chinese Physics B,2021(3). |
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| Authors: | Yu-Guo Su Fei Yao Hong-Bin Liang Yan-Ming Che Li-Bin Fu Xiao-Guang Wang |
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| Affiliation: | (Zhejiang Province Key Laboratory of Quantum Technology and Device,Department of Physics,Zhejiang University,Hangzhou 310027,China;National Laboratory of Science and Technology on Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China) |
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| Abstract: | By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space. However, the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet. Here, a practical method is presented to resolve the problem for the mixed-spin(s, 1/2) system and describe the entanglement of the system. The system can be decomposed into two spins: spin-(s + 1/2) and spin-(s-1/2) at the coupling bases, which can be regarded as independent spins. Besides, any pure state may be written as a superposition of two orthonormal states with one spin-(s + 1/2) state and the other spin-(s-1/2) state. Thus, the whole initial state can be regarded as a state of a pseudo spin-1/2. In this way, the mixed spin decomposes into three spins.Therefore, the state can be represented by(2 s + 1) +(2 s-1) + 1 = 4 s + 1 sets of stars on a Bloch sphere. Finally, some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere. |
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