Generalized spin bases for quantum chemistry and quantum information
M. Kibler
备注：
Dedicated to Professor Rudolf Zahradnik on the occasion of his 80th birthday. Invited paper to be published in Collection of Czechoslovak Chemical Communications
发表信息：
Collection of Czechoslovak Chemical Communications 73 (2008) 1281-1298
Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation. Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mutually unbiased bases in the case where the dimension d of the considered Hilbert subspace is a prime number. We also give the starting point for studying the case where d is the power of a prime number. A connection of this work with the unitary group U(d) and the Pauli group is brielly underlined.
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Next Generation Computing, BASF SE（巴斯夫股份公司下一代计算部门）；The Volgenau Department of Physics, United States Naval Academy（美国海军学院沃尔格瑙物理系）；Department of Physics, Harvard University（哈佛大学物理系）
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