标题： 互不偏置基：自旋态的层析成像和星积方案 显示英文标题

标题： Mutually unbiased bases: tomography of spin states and star-product scheme

摘要： 在通用星积方案的框架内考虑了相互无偏基（MUBs）。我们重新推导出，一组完整的MUBs适用于自旋层析成像，即了解系统在每个MUB态中的所有概率就足以进行状态重建。将层析概率表示和星积方案的思想扩展到MUB层析成像，引入了自旋态和算符的MUB符号的去量化器和量化器算符，找到了普通和对偶的星积核。由于MUB投影算符需要遵循星积方案的特定规则，我们揭示了MUB投影算符的李代数结构，并推导出关于MUB投影算符三重积和四重积的新关系。详细考虑了量子比特的例子。讨论了通过斯特恩-格拉赫装置进行的MUB层析成像。 显示英文摘要

摘要： Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.