复合系统有限Heisenberg群的对称性
Symmetries of the finite Heisenberg group for composite systems
摘要：
有限海森堡群的对称性是研究有限维量子力学深层结构的重要工具。众所周知，这些对称性可以用特定的正规化子来表示。本文将以前的研究扩展到由两个具有任意维数n和m的子系统qudits组成的复合量子系统。在本文中，我们提出了详细的描述-在GL（nm，C）的内自同构群-的阿贝尔子群的正规化子所产生的张量积的广义泡利矩阵的n和m阶。对称群则由正规化子的商群给出。
英文摘要：
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.
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